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This article outlines a method for automatically generating models of dynamic decision-making that both have strong predictive power and are interpretable in human terms. This is useful for designing empirically grounded agent-based…

Machine Learning · Statistics 2016-11-17 John J. Nay , Jonathan M. Gilligan

Data-driven discovery of governing equations is of great significance for helping us understand intrinsic mechanisms and build physical models. Recently, numerous highly innovative algorithms have emerged, aimed at inversely discovering the…

Data Analysis, Statistics and Probability · Physics 2024-03-29 Wenjun Ma , Jun Zhang , Kaikai Feng , Haoyun Xing , Dongsheng Wen

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Machine Learning · Computer Science 2021-09-14 Hao Xu , Dongxiao Zhang , Nanzhe Wang

As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically…

Machine Learning · Computer Science 2024-10-11 Kevin Zhang , Hod Lipson

Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…

Machine Learning · Computer Science 2023-01-11 Daniel Floryan , Michael D. Graham

Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less…

Numerical Analysis · Mathematics 2020-09-25 Jia Zhao , Jarrod Mau

We propose a data-driven algorithm for numerical invariant synthesis and verification. The algorithm is based on the ICE-DT schema for learning decision trees from samples of positive and negative states and implications corresponding to…

Programming Languages · Computer Science 2022-07-11 Ahmed Bouajjani , Wael-Amine Boutglay , Peter Habermehl

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

Machine Learning · Computer Science 2023-05-01 Zijie Li , Kazem Meidani , Amir Barati Farimani

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

Machine Learning · Computer Science 2021-03-30 Pawan Goyal , Peter Benner

We present a deep generative model that learns disentangled static and dynamic representations of data from unordered input. Our approach exploits regularities in sequential data that exist regardless of the order in which the data is…

Machine Learning · Statistics 2018-12-11 Leonhard Helminger , Abdelaziz Djelouah , Markus Gross , Romann M. Weber

Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased…

Machine Learning · Computer Science 2022-10-12 Pawan Goyal , Peter Benner

Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are…

Materials Science · Physics 2025-11-14 Hao Xu , Yuntian Chen , Dongxiao Zhang

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Dynamical Systems · Mathematics 2026-05-07 Nibodh Boddupalli , Timothy Matchen , Jeff Moehlis

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

Numerical Analysis · Mathematics 2024-03-11 Tracey Oellerich , Maria Emelianenko

Understanding an opponent agent helps in negotiating with it. Existing works on understanding opponents focus on preference modeling (or estimating the opponent's utility function). An important but largely unexplored direction is…

Artificial Intelligence · Computer Science 2021-10-08 Ming Li , Pradeep K. Murukannaiah , Catholijn M. Jonker

Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we…

Machine Learning · Computer Science 2026-01-22 Zhongyi Jiang , Chunmei Wang , Haizhao Yang

Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…

Optimization and Control · Mathematics 2025-07-08 Vincent Roulet , Siddhartha Srinivasa , Maryam Fazel , Zaid Harchaoui

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…

Neural and Evolutionary Computing · Computer Science 2016-11-16 Dario Izzo , Francesco Biscani , Alessio Mereta

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Systems and Control · Computer Science 2019-03-01 Ibrahim Ayed , Emmanuel de Bézenac , Arthur Pajot , Julien Brajard , Patrick Gallinari

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…

Computational Physics · Physics 2018-03-05 L. Felsberger , P. S. Koutsourelakis