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Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Assessing progress toward the Sustainable Development Goals (SDGs) requires multi-step reasoning over visual cues, contextual knowledge, and development indicators, where incomplete evidence use and imperfect evidence integration can…

Computer Vision and Pattern Recognition · Computer Science 2026-05-22 Zihang Lin , Huaiyuan Qin , Muli Yang , Hongyuan Zhu

Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…

Machine Learning · Computer Science 2020-12-22 Waad Subber , Piyush Pandita , Sayan Ghosh , Genghis Khan , Liping Wang , Roger Ghanem

Equation discovery from data is a central challenge in machine learning for science, which requires the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent large language model (LLM)…

Machine Learning · Computer Science 2026-03-04 Sanchit Kabra , Shobhnik Kriplani , Parshin Shojaee , Chandan K. Reddy

In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained…

Optimization and Control · Mathematics 2025-09-23 Mohsen Sadr , Tony Tohme , Kamal Youcef-Toumi

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Machine Learning · Computer Science 2023-03-17 Mengge Du , Yuntian Chen , Dongxiao Zhang

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

Machine Learning · Computer Science 2025-04-14 Krzysztof Kacprzyk , Mihaela van der Schaar

Time series anomaly detection is a vital task in many domains, including patient monitoring in healthcare, forecasting in finance, and predictive maintenance in energy industries. This has led to a proliferation of anomaly detection…

Machine Learning · Computer Science 2024-11-26 Sarah Alnegheimish , Laure Berti-Equille , Kalyan Veeramachaneni

Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…

Machine Learning · Statistics 2026-03-25 Arno Strouwen , Sebastian Micluţa-Câmpeanu

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

Methodology · Statistics 2023-09-01 Itai Dattner , Shota Gugushvili , Oleksandr Laskorunskyi

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex…

Machine Learning · Computer Science 2025-04-15 Junfeng Chen , Kailiang Wu , Dongbin Xiu

A variety of established approaches exist for the detection of dynamic bottlenecks. Furthermore, the prediction of bottlenecks is experiencing a growing scientific interest, quantifiable by the increasing number of publications in recent…

Systems and Control · Electrical Eng. & Systems 2023-06-29 Nikolai West , Joern Schwenken , Jochen Deuse

Process-level Reward Models (PRMs) are crucial for complex reasoning and decision-making tasks, where each intermediate step plays an important role in the reasoning process. Since language models are prone to various types of errors during…

Computation and Language · Computer Science 2025-07-01 Mingyang Song , Zhaochen Su , Xiaoye Qu , Jiawei Zhou , Yu Cheng

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…

Machine Learning · Computer Science 2019-07-02 Nikola Simidjievski , Ljupčo Todorovski , Juš Kocijan , Sašo Džeroski

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…

Machine Learning · Statistics 2021-11-25 Georges Tod , Gert-Jan Both , Remy Kusters

Recovering editable CAD programs from images or 3D observations is central to AI-assisted design, but progress is difficult to measure because existing evaluations are fragmented across datasets, modalities, and metrics. We introduce…

Computer Vision and Pattern Recognition · Computer Science 2026-05-12 Anna C. Doris , Jacob Thomas Sony , Ghadi Nehme , Era Syla , Amin Heyrani Nobari , Faez Ahmed

Data-driven modeling of fluid dynamics has advanced rapidly with neural PDE solvers, yet a fair and strong benchmark remains fragmented due to the absence of unified PDE datasets and standardized evaluation protocols. Although architectural…

Fluid Dynamics · Physics 2026-05-22 Haixin Wang , Ruoyan Li , Fred Xu , Fang Sun , Kaiqiao Han , Zijie Huang , Ching Chang , Xiao Luo , Wei Wang , Yizhou Sun

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…

Machine Learning · Computer Science 2025-10-13 Benjamin Herdeanu , Juan Nathaniel , Carla Roesch , Jatan Buch , Gregor Ramien , Johannes Haux , Pierre Gentine

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Methodology · Statistics 2025-05-20 Qingchuan Sun , Susanne Ditlevsen

Current model structural discovery methods for power system dynamics impose rigid priors on the basis functions and variable sets of dynamic models while often neglecting algebraic constraints, thereby limiting the formulation of…

Systems and Control · Electrical Eng. & Systems 2026-01-12 Chao Shen , Zihan Guo , Ke Zuo , Wenqi Huang , Mingyang Sun