It's the Most Terrible Time of the Year is an AI-generated television commercial created for McDonald's Netherlands by TBWA\Neboko and The Sweetshop. It was released on 6 December 2025 before being pulled four days later due to negative reception over its use of generative artificial intelligence and its cynical, negative depiction of the holiday season. == Plot == On a bleak, snowy day, various people in the city experience different kinds of mishaps during the Christmas season. Among other incidents, families struggle with their huge loads of presents; Santa Claus gets stuck in traffic; a Christmas tree "redecorates" a man's home, sending him through the window; another family puts up with annoying relatives and a burnt Christmas dinner. Because of all this chaos, a man decides to find refuge in a McDonald's outlet. A Christmas choir finishes singing the jingle "It's the Most Terrible Time of the Year" with the call to action to "hide out in McDonald's till January's here". == Campaign == It's the Most Terrible Time of the Year is a 45-second television commercial made by Dutch agency TBWA\Neboko with involvement of United States-based film production studio The Sweetshop. The advertisement was produced heavily with generative artificial intelligence (AI) following the trend set by other brands such as Coca-Cola and Toys "R" Us. McDonald's Netherlands, the client, released a statement that the commercial was meant to depict "the stressful moments during the holidays in the Netherlands". The commercial also used Andy Williams's "It's the Most Wonderful Time of the Year" with lyrics changed to fit with the concept of the advertisement. According to The Sweetshop, the production of the advertisement took "seven weeks". It also added that much effort was put into the commercial compared to the traditional process. Ten people of its in-house AI engine The Gardening Club worked on the project. Los Angeles-based directors Mark Potoka and Matt Spicer were initially credited to be involved in the film but they resigned due to being sidelined from the production process. == Reception == The advertisement was released on McDonald's Netherlands' YouTube channel on 6 December 2025. It had a negative reception over the use of generative AI and the "cynical" concept of the work's story. The video was made private on 9 December 2025. The Sweetshop stated that the production of the advertisement took human effort. McDonald's Netherlands, while stating the original intent of the commercial, released a statement after its pullout that, for many of its customers, the holiday season is the "most wonderful time of the year".
Retrieval-augmented generation (RAG) is a technique that enables large language models (LLMs) to retrieve and incorporate new information from external data sources. With RAG, LLMs first refer to a specified set of documents, then respond to user queries. These documents supplement information from the LLM's pre-existing training data. This allows LLMs to use domain-specific and/or updated information that is not available in the training data. For example, this enables LLM-based chatbots to access internal company data or generate responses based on authoritative sources. RAG improves LLMs by incorporating information retrieval before generating responses. Unlike LLMs that rely on static training data, RAG pulls relevant text from databases, uploaded documents, or web sources. According to Ars Technica, "RAG is a way of improving LLM performance, in essence by blending the LLM process with a web search or other document look-up process to help LLMs stick to the facts." This method helps reduce AI hallucinations, which have caused chatbots to describe policies that don't exist, or recommend nonexistent legal cases to lawyers that are looking for citations to support their arguments. RAG also reduces the need to retrain LLMs with new data, saving on computational and financial costs. Beyond efficiency gains, RAG also allows LLMs to include sources in their responses, so users can verify the cited sources. This provides greater transparency, as users can cross-check retrieved content to ensure accuracy and relevance. The term retrieval-augmented generation (RAG) was introduced in a 2020 paper that described combining a parametric language model with a non-parametric external memory accessed through retrieval at inference time. == RAG and LLM limitations == LLMs can provide incorrect information. For example, when Google first demonstrated its LLM tool "Google Bard" (later re-branded to Gemini), the LLM provided incorrect information about the James Webb Space Telescope. This error contributed to a $100 billion decline in Google's stock value. RAG is used to prevent these errors, but it does not solve all the problems. For example, LLMs can generate misinformation even when pulling from factually correct sources if they misinterpret the context. MIT Technology Review gives the example of an AI-generated response stating, "The United States has had one Muslim president, Barack Hussein Obama." The model retrieved this from an academic book rhetorically titled Barack Hussein Obama: America's First Muslim President? The LLM did not "know" or "understand" the context of the title, generating a false statement. LLMs with RAG are programmed to prioritize new information. This technique has been called "prompt stuffing." Without prompt stuffing, the LLM's input is generated by a user; with prompt stuffing, additional relevant context is added to this input to guide the model's response. This approach provides the LLM with key information early in the prompt, encouraging it to prioritize the supplied data over pre-existing training knowledge. == Process == Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating an information-retrieval mechanism that allows models to access and utilize additional data beyond their original training set. Ars Technica notes that "when new information becomes available, rather than having to retrain the model, all that's needed is to augment the model's external knowledge base with the updated information" ("augmentation"). IBM states that "in the generative phase, the LLM draws from the augmented prompt and its internal representation of its training data to synthesize" an answer. === RAG key stages === Typically, the data to be referenced is converted into LLM embeddings, numerical representations in the form of a large vector space. RAG can be used on unstructured (usually text), semi-structured, or structured data (for example knowledge graphs). These embeddings are then stored in a vector database to allow for document retrieval. Given a user query, a document retriever is first called to select the most relevant documents that will be used to augment the query. This comparison can be done using a variety of methods, which depend in part on the type of indexing used. The model feeds this relevant retrieved information into the LLM via prompt engineering of the user's original query. Newer implementations (as of 2023) can also incorporate specific augmentation modules with abilities such as expanding queries into multiple domains and using memory and self-improvement to learn from previous retrievals. Finally, the LLM can generate output based on both the query and the retrieved documents. Some models incorporate extra steps to improve output, such as the re-ranking of retrieved information, context selection, and fine-tuning. == Applications == Retrieval-augmented generation is used in applications where generated responses need to be grounded in external or frequently updated information. Commonly cited use cases include search engines, question-answering systems, customer support chatbots, enterprise knowledge assistants, content generation, recommendation systems, retail and e-commerce, and industrial or manufacturing workflows. In healthcare, RAG has been studied as a way to ground large language model outputs in external medical knowledge sources, although reviews have noted continuing challenges around evaluation, ethics, and clinical reliability. == Improvements == Improvements to the basic process above can be applied at different stages in the RAG flow. === Encoder === These methods focus on the encoding of text as either dense or sparse vectors. Sparse vectors, which encode the identity of a word, are typically dictionary-length and contain mostly zeros. Dense vectors, which encode meaning, are more compact and contain fewer zeros. Various enhancements can improve the way similarities are calculated in the vector stores (databases). Performance improves by optimizing how vector similarities are calculated. Dot products enhance similarity scoring, while approximate nearest neighbor (ANN) searches improve retrieval efficiency over K-nearest neighbors (KNN) searches. Accuracy may be improved with Late Interactions, which allow the system to compare words more precisely after retrieval. This helps refine document ranking and improve search relevance. Hybrid vector approaches may be used to combine dense vector representations with sparse one-hot vectors, taking advantage of the computational efficiency of sparse dot products over dense vector operations. Other retrieval techniques focus on improving accuracy by refining how documents are selected. Some retrieval methods combine sparse representations, such as SPLADE, with query expansion strategies to improve search accuracy and recall. === Retriever-centric methods === These methods aim to enhance the quality of document retrieval in vector databases: Pre-training the retriever using the Inverse Cloze Task (ICT), a technique that helps the model learn retrieval patterns by predicting masked text within documents. Supervised retriever optimization aligns retrieval probabilities with the generator model's likelihood distribution. This involves retrieving the top-k vectors for a given prompt, scoring the generated response's perplexity, and minimizing KL divergence between the retriever's selections and the model's likelihoods to refine retrieval. Reranking techniques can refine retriever performance by prioritizing the most relevant retrieved documents during training. === Language model === By redesigning the language model with the retriever in mind, a 25-time smaller network can get comparable perplexity as its much larger counterparts. Because it is trained from scratch, this method (Retro) incurs the high cost of training runs that the original RAG scheme avoided. The hypothesis is that by giving domain knowledge during training, Retro needs less focus on the domain and can devote its smaller weight resources only to language semantics. The redesigned language model is shown here. It has been reported that Retro is not reproducible, so modifications were made to make it so. The more reproducible version is called Retro++ and includes in-context RAG. === Chunking === Chunking involves various strategies for breaking up the data into vectors so the retriever can find details in it. Three types of chunking strategies are: Fixed length with overlap. This is fast and easy. Overlapping consecutive chunks helps to maintain semantic context across chunks. Syntax-based chunks can break the document up into sentences. Libraries such as spaCy or NLTK can also help. File format-based chunking. Certain file types have natural chunks built in, and it's best to respect them. For example, code files are best chunked and vectorized as whole functions or classes. HTML files should leave
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to get from point A to B) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science, engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias, mental set, and functional fixedness. == Definition == The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. === Psychology === Problem solving in psychology refers to the process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study the human problem-solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization,human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. === Cognitive sciences === Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known is the work of Allen Newell and Herbert A. Simon. Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi, admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved. An outstanding problem-solving technique found by this research is the principle of decomposition. === Computer science === Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation. A large, perennial obstacle is to find and fix errors in computer programs: debugging. === Logic === Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. === Engineering === When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypothes
Edge inference is the process of running machine learning or deep learning models on local devices (edge devices) such as smartphones, IoT devices, embedded systems, and edge servers instead of centralized cloud computing infrastructure. A key feature of edge computing is edge inference, which allows for real-time data processing, low latency, and improved privacy by reducing the amount of data sent to remote servers.
Machine unlearning is a branch of machine learning focused on removing specific undesired element, such as private data, wrong or manipulated training data, outdated information, copyrighted material, harmful content, dangerous abilities, or misinformation, without needing to rebuild models from the ground up. Large language models, like the ones powering ChatGPT, may be asked not just to remove specific elements but also to unlearn a "concept," "fact," or "knowledge," which aren't easily linked to specific examples. New terms such as "model editing," "concept editing," and "knowledge unlearning" have emerged to describe this process. == History == Early research efforts were largely motivated by Article 17 of the GDPR, the European Union's privacy regulation commonly known as the "right to be forgotten" (RTBF), introduced in 2014. The GDPR did not anticipate that the development of large language models would make data erasure a complex task. This issue has since led to research on "machine unlearning," with a growing focus on removing copyrighted material, harmful content, dangerous capabilities, and misinformation. Just as early experiences in humans shape later ones, some concepts are more fundamental and harder to unlearn. A piece of knowledge may be so deeply embedded in the model's knowledge graph that unlearning it could cause internal contradictions, requiring adjustments to other parts of the graph to resolve them. Researchers have now also started studying unlearning in the context of removing incorrect or adversarially manipulated training data such as systematically biased labels or poisoning attacks. == Motivations == At present, machine unlearning is motivated by a growing range of concerns that extend well beyond the field's original focus on data privacy. A widely used taxonomy in the literature distinguishes two high-level categories of motivation. Access revocation covers cases where a data subject or rights holder requests the removal of data they own or control. This is most commonly associated with RTBF established by the European Union's General Data Protection Regulation (GDPR) and analogous legislation such as the California Consumer Privacy Act (CCPA). These regulations grant individuals the legal right to request erasure of their personal data from any system that has processed it, including models that were trained on it. Access revocation also encompasses the removal of copyrighted or pay-walled content that was incorporated into training corpora without the necessary licenses, a concern that has become prominent with the widespread use of largely web-scraped pre-training datasets. Model correction covers cases where the model exhibits undesirable behavior arising from the training data, regardless of any individual's request. This includes: Removal of toxic, biased, or unsafe outputs introduced by harmful content in the training set Correction of stale or factually incorrect associations, such as outdated knowledge encoded in a deployed model Removal of dangerous capabilities, such as detailed knowledge of the synthesis of chemical or biological agents Correction of the influence of data poisoning or adversarial attacks that have corrupted model behavior This second category has been formalized as corrective machine unlearning, which frames unlearning as a post-training mechanism for repairing the effects of bad or harmful training data. It is closely related to the AI safety literature, where data filtering alone has been found insufficient to prevent hazardous knowledge from being encoded in model weights, motivating unlearning as a complementary risk mitigation strategy. A further distinction has been drawn in the literature between removal {eliminating the influence of specific training data on model parameters) and suppression (preventing the model from generating specific outputs regardless of how that knowledge is encoded). These two goals are not equivalent: removing training data does not guarantee meaningful output suppression, and suppressing outputs does not constitute removal of the underlying training data's influence. == SISA Training == SISA is a training strategy consisting of four mechanisms designed to make machine unlearning more efficient by structuring how models are trained and updated. Its goal is to allow a system to remove the influence of specific data points without retraining an entire model from scratch. By reorganizing training data and workflows, SISA reduces the computational burden of unlearning requests. Sharding divides the training dataset into multiple disjoint subsets, or shards. Each shard is used to train a separate model instance. This ensures that a single data point affects only one shard, so unlearning it requires updating only the corresponding shard rather than the full model. Isolation refers to training each shard independently, with nothing shared across shards during the training process. This separation prevents cross-contamination between shards, ensuring that forgetting data in one shard does not require adjustments to any others. Slicing breaks the data within each shard into sequential slices and stores model states after each slice is trained on. When an unlearning request targets a piece of data, the system can roll back to the checkpoint before the point was seen and retrain only from that slice forward. This reduces retraining time even within a shard. Aggregation occurs at inference, when the model is queried. It combines the outputs of each shard to determine the output of the overall model. This is often through majority voting or averaging. This allows SISA-trained systems to behave like a single model despite being composed of multiple shard-level models. Together, these mechanisms enable machine learning systems to forget specific data points with far lower computational cost than full retraining. The trade-off is that sharding and slicing can lead to reduced model accuracy, worse generalization, and increased storage requirements for the intermediate checkpoints. This can be tolerable based on the needs of the individual or organization to comply with "right to be forgotten" or efficiently recover from backdoor attacks. == Algorithms == Machine unlearning algorithms are broadly categorized into exact and approximate methods, reflecting a fundamental trade-off between formal guarantees and computational tractability. === Exact Unlearning === Exact unlearning methods produce a model that is statistically indistinguishable from one retrained from scratch on the dataset with the forget data removed. The canonical framework for exact unlearning is SISA Training (Sharded, Isolated, Sliced, and Aggregated), introduced by Bourtoule et al. (2021). SISA partitions the training dataset into disjoint shards and trains a separate sub-model on each. At inference time, predictions are aggregated across sub-models. When an unlearning request is received, only the sub-model corresponding to the shard containing the target data requires retraining, reducing computational overhead proportionally to the number of shards. Exact methods provide the strongest guarantees but become prohibitively expensive for large pre-trained neural networks and are generally limited to settings where training can be structured in advance. === Approximate Unlearning === Approximate unlearning methods seek to produce a model whose behavior is sufficiently close to an exactly unlearned model without the cost of full retraining. These methods dominate practical applications. Common approaches include: Gradient Ascent: The model is fine-tuned by maximizing the loss on the forget set, directly degrading its performance on targeted data. This is the most direct approach but risks destabilizing performance on retained data. Random Labelling: The model is fine-tuned on the forget set using randomly shuffled labels, confusing its associations with the targeted data while producing a less aggressive weight shift than pure gradient ascent. Gradient Difference: Combines gradient ascent on the forget set with simultaneous gradient descent on the retain set, using the retain objective as a regularizer to preserve general model utility. KL Divergence Regularization: Minimizes the KL divergence between the outputs of the unlearned model and the original model on the retain set, anchoring behavior on data the model should remember. Weight Pruning and Fine-tuning: Parameters with the smallest L1-norm are pruned — targeting weights most weakly associated with general knowledge and potentially most associated with the forget set — followed by fine-tuning on the retain set to restore utility. Layer Reset and Fine-tuning: The first or last k layers are re-initialized to random weights and the model is subsequently fine-tuned on the retain set. This is a coarse but computationally simple approach. Selective Synaptic Dampening: Uses influence functions to estimate the effect of individual trainin
Radar geo-warping is the adjustment of geo-referenced radar images and video data to be consistent with a geographical projection. This image warping avoids any restrictions when displaying it together with video from multiple radar sources or with other geographical data including scanned maps and satellite images which may be provided in a particular projection. There are many areas where geo warping has unique benefits: Single radar video signal displayed together with maps of different geographical projections. E.g. Mercator UTM stereographic Multiple radar video signals displayed simultaneously: Having the computing power to do so on one computer. Adapting the projection of all radar signals allowing the geographically correct display and accurate superimposition of those videos. Slant range correction: a modern 3D radar system can measure the height of a target and hence it is possible to correct the radar video by the real corrected range of the target. Slant Range Correction also allows to compensate the radar tower height e.g. for maritime surveillance radars. == Introduction == Radar video presents the echoes of electromagnetic waves a radar system has emitted and received as reflections afterwards. These echoes are typically presented on a computer screen with a color-coding scheme depicting the reflection strength. Two problems have to be solved during such a visualization process. The first problem arises from the fact that typically the radar antenna turns around its position and measures the reflection echo distances from its position in one direction. This effectively means that the radar video data are present in polar coordinates. In older systems the polar oriented picture has been displayed in so called plan position indicators (PPI). The PPI-scope uses a radial sweep pivoting about the center of the presentation. This results in a map-like picture of the area covered by the radar beam. A long-persistence screen is used so that the display remains visible until the sweep passes again. Bearing to the target is indicated by the target's angular position in relation to an imaginary line extending vertically from the sweep origin to the top of the scope. The top of the scope is either true north (when the indicator is operated in the true bearing mode) or ship's heading (when the indicator is operated in the relative bearing mode). For visualization on a modern computer screen the polar coordinates have to be converted into Cartesian coordinates. This process called radar scan conversion is presented with more detail in the next section. The second problem to solve arises from the fact that a radar system is placed in the real world and measures real world echo positions. These echoes have to be displayed together with other real world data like object positions, vector maps and satellite images in a consistent way. All this information refers to the curved earth surface but is displayed on a flat computer display. Building a link from real world earth positions to display pixels is commonly called geographical referencing or in short geo-referencing. Part of the geo-referencing process is to map the 3D earth surface onto a 2D display. This process of a geographical projection can be performed in many ways, but different data sources have their own 'natural' projection. E.g. Cartesian radar video data from a radar source on the earth surface are geo-referenced by a so-called radar projection. When using this radar projection the Cartesian radar video pixels can directly displayed on a computer screen (only being linearly transformed according to the current position on the screen and e.g. the current zoom level). A problem now arises if e.g. also a satellite map shall be shown together with the radar video data. The 'natural' geographical projection of a satellite image would be a satellite projection which depends on the satellite orbit, position and further parameters. Now either the satellite image has to be reprojected to a radar projection or the radar video has to use the satellite projection. This geographical re-projection is also called geographical warping or Geo Warping where each image pixel has to be transformed from one projection into another. This article describes in further detail the Geo Warping of radar video images in real time. It will also show that radar video Geo Warping is done most efficiently when it is integrated with the radar scan conversion process. == Radar-scan conversion == This section describes the principles of the radar-scan conversion (RSC) process. The radar supplies its measured data in polar coordinates (ρ,θ) directly from the rotating antenna. ρ defines the target/echo distance and θ the target angle in polar world coordinates. These data are measured, digitized and stored in a polar coordinate polar store or polar pixmap. The main RSC task is to convert these data to Cartesian (x, y) display coordinates, creating the necessary display pixels. The RSC process is influenced by the current zoom, shift and rotation settings defining which part of the 'world' shall be visible in the display image. As detailed later the RSC process also takes the currently used geographical projection into account when the radar video images are Geo Warped. The OpenGL RSC is implemented using a reverse scan conversion approach which calculates for every image pixel the most appropriate radar amplitude value in the polar store. This approach generates an optimal image without any artifacts known from forward spoke fill algorithms. By applying bi-linear filtering between adjacent pixels in the polar store during the conversion process the OpenGL RSC finally achieves a very high visual quality radar display image for every zoom level, creating smooth images of the radar echoes. == Radar projection == This section illustrates how radar video data are geo referenced and displayed on a computer screen. The radar sensor is positioned on the earth surface with a height h above the ground. It measures the direct distance d to the target (and not e.g. the distance the target is away from the radar if one would move on the earth surface). This distance is then used in the display plane after adjustment to the current display zoom level by the radar scan converter (RSC). Now it has to be clarified how the radar video data is geo referenced. This basically means, that if we want to display a geographical real world object (like e.g. a light house) which is at the same real world position as the radar target, that it also shall appear at the same position in the display plane. This is realized by calculating the distance from the radar sensor to the respective real world object and use that distance in the display plane. The position of the real world object is typically given in geographical coordinates (latitude, longitude and height above the earth surface). In other words, using a radar projection with geographical data is done by simulating a radar measurement process with the real world objects and use the resulting range and azimuth in the display plane. The second picture to the right shows an example radar projection with the center of projection (COP) at latitude 50.0° and longitude 0.0° which is also the radar position. The dashed lines are the equal-latitude and equal-longitude lines on top of the background map. The solid lines show equal-range and equal-azimuth with the respect to the radar position. It is a feature of the radar projection that equal-range lines are circles and equal-azimuth lines are straight lines. This is necessary to display radar video consistently with other map data when using a radar projection where the projection center has to be the radar position. == Geo Warping process == This section explains the actual geo warping or re-projection process when applied to radar video in real time. Assume we want to display radar video on top of a satellite image. As an example we use the CIB projection which is used to display satellite data in CIB (Controlled Image Base) format. The Figure Geo Warping Radar to CIB Projection shows dashed the maximal range circle for a range of 111 km or 60 miles using the radar projection. Such a range is typical for long range coastal surveillance radars. As stated in the last section this is a perfect circle also on the computer screen. The solid line ellipse shows the same range circle for the CIB projection. Typically the errors occurring without Geo Warping are smallest near the radar position if at least the projection center (COP) coincides with the radar position, as realized in our example. Otherwise the error distribution depends both on the used projection and also on the projection parameters. Thus, in our case the errors are most significant near the maximum radar range. The CIB projection error corrected in east–west direction at half the radar range is 2.6 km and is 5.3 km at the full radar range of 111 km. An error of 5.3 km is
Machine-learned interatomic potentials (MLIPs), or simply machine learning potentials (MLPs), are interatomic potentials constructed using machine learning. Beginning in the 1990s, researchers have employed such programs to construct interatomic potentials by mapping atomic structures to their potential energies. These potentials are referred to as MLIPs or MLPs. Such machine learning potentials promised to fill the gap between density functional theory, a highly accurate but computationally intensive modelling method, and empirically derived or intuitively-approximated potentials, which were far lighter computationally but substantially less accurate. Improvements in artificial intelligence technology heightened the accuracy of MLPs while lowering their computational cost, increasing the role of machine learning in fitting potentials. Machine learning potentials began by using neural networks to tackle low-dimensional systems. While promising, these models could not systematically account for interatomic energy interactions; they could be applied to small molecules in a vacuum, or molecules interacting with frozen surfaces, but not much else – and even in these applications, the models often relied on force fields or potentials derived empirically or with simulations. These models thus remained confined to academia. Modern neural networks construct highly accurate and computationally light potentials, as theoretical understanding of materials science was increasingly built into their architectures and preprocessing. Almost all are local, accounting for all interactions between an atom and its neighbor up to some cutoff radius. There exist some nonlocal models, but these have been experimental for almost a decade. For most systems, reasonable cutoff radii enable highly accurate results. Almost all neural networks intake atomic coordinates and output potential energies. For some, these atomic coordinates are converted into atom-centered symmetry functions. From this data, a separate atomic neural network is trained for each element; each atomic network is evaluated whenever that element occurs in the given structure, and then the results are pooled together at the end. This process – in particular, the atom-centered symmetry functions which convey translational, rotational, and permutational invariances – has greatly improved machine learning potentials by significantly constraining the neural network search space. Other models use a similar process but emphasize bonds over atoms, using pair symmetry functions and training one network per atom pair. Other models to learn their own descriptors rather than using predetermined symmetry-dictating functions. These models, called message-passing neural networks (MPNNs), are graph neural networks. Treating molecules as three-dimensional graphs (where atoms are nodes and bonds are edges), the model takes feature vectors describing the atoms as input, and iteratively updates these vectors as information about neighboring atoms is processed through message functions and convolutions. These feature vectors are then used to predict the final potentials. The flexibility of this method often results in stronger, more generalizable models. In 2017, the first-ever MPNN model (a deep tensor neural network) was used to calculate the properties of small organic molecules. == Gaussian Approximation Potential (GAP) == One popular class of machine-learned interatomic potential is the Gaussian Approximation Potential (GAP), which combines compact descriptors of local atomic environments with Gaussian process regression to machine learn the potential energy surface of a given system. To date, the GAP framework has been used to successfully develop a number of MLIPs for various systems, including for elemental systems such as carbon, silicon, phosphorus, and tungsten, as well as for multicomponent systems such as Ge2Sb2Te5 and austenitic stainless steel, Fe7Cr2Ni. == Equivariant graph neural networks == A significant limitation of early MPNNs was that they were not inherently equivariant to rotations and reflections of atomic structures — meaning predictions could change depending on how a molecule was oriented in space. Beginning around 2021, a new class of models addressed this by incorporating equivariance directly into the message-passing layers using spherical harmonics and irreducible representations. Notable examples include NequIP (2021), MACE (2022), and GemNet-OC (2022). These equivariant architectures proved substantially more data-efficient and accurate than their predecessors, and became the dominant paradigm for high-accuracy MLIPs. == Universal MLIPs and large-scale datasets == Early MLIPs were system-specific, trained on a few thousand structures of a single material. A major shift occurred with the creation of large, chemically diverse datasets enabling models that generalize across many elements, bonding environments, and application domains — so-called universal MLIPs. A key driver was the Open Catalyst Project (OC20, OC22), a collaboration between Meta AI (FAIR) and Carnegie Mellon University launched in 2020. OC20 comprises approximately 1.3 million DFT relaxations across 82 elements, designed to accelerate the discovery of catalysts for renewable energy applications. It was among the first datasets large enough to train GNNs that generalize across diverse chemical systems, and established a widely-used benchmark for the field. A subsequent dataset, Open Direct Air Capture (OpenDAC 2023 and OpenDAC 2025), applied the same approach to carbon capture, providing a large computational database of metal-organic frameworks and sorbent candidates evaluated for CO₂ capture, generated using nearly 400 million CPU hours of quantum chemistry calculations in collaboration with Georgia Tech. These datasets revealed a new challenge: the GNN architectures most effective for atomic simulations were memory-intensive, as they model higher-order interactions between triplets or quadruplets of atoms, making it difficult to scale model size. Graph Parallelism, introduced by Sriram et al. (ICLR 2022), addressed this by distributing a single input graph across multiple GPUs — a distinct strategy from data parallelism (which distributes training examples) or model parallelism (which distributes layers). This enabled training GNNs with hundreds of millions to billions of parameters for the first time. Building on these foundations, Meta FAIR released the Universal Model for Atoms (UMA) in 2025, trained on approximately 500 million unique 3D atomic structures spanning molecules, materials, and catalysts — the largest training run to date for an MLIP. UMA introduced a Mixture of Linear Experts (MoLE) architecture, enabling one model to learn from datasets generated by different DFT codes and settings without significant inference overhead. It matches or surpasses specialized models across catalysis, materials, and molecular benchmarks without task-specific fine-tuning, and has been described as marking a "pre/post-UMA" divide in the field. == Applications == Catalyst discovery: MLIPs have significantly accelerated the computational screening of heterogeneous catalysts by replacing expensive DFT relaxations with fast neural network surrogates. The Open Catalyst Project explicitly targets this application, aiming to identify new catalysts for green hydrogen production and other renewable energy reactions. Carbon capture: The OpenDAC project applies universal MLIPs to screening sorbent materials for direct air capture of CO₂, a key technology for climate change mitigation. AI-accelerated screening allows evaluation of orders of magnitude more candidate materials than traditional DFT workflows. Drug discovery and molecular design: MLIPs are increasingly used in pharmaceutical research to model molecular conformations and binding energies. The Open Molecules 2025 (OMol25) dataset, released by Meta FAIR in 2025, provides high-accuracy calculations for a large set of molecular systems to support this use case. Materials discovery: Universal MLIPs enable high-throughput screening of novel inorganic materials, including battery electrolytes, semiconductors, and superconductors, by rapidly estimating stability and properties across large chemical spaces.
