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The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Artificial Intelligence · Computer Science 2021-03-03 Hikaru Shindo , Masaaki Nishino , Akihiro Yamamoto

We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data. This is, of course, a classical…

Machine Learning · Statistics 2020-11-18 Hassan Arbabi , Felix P. Kemeth , Tom Bertalan , Ioannis Kevrekidis

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

Machine Learning · Statistics 2025-04-07 Yasamin Jalalian , Juan Felipe Osorio Ramirez , Alexander Hsu , Bamdad Hosseini , Houman Owhadi

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to…

Artificial Intelligence · Computer Science 2023-02-27 Tineke Blom , Joris M. Mooij

Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this…

Soft Condensed Matter · Physics 2025-02-05 Ryota Watanabe , Takanori Ishii , Yuji Hirono , Hirokazu Maruoka

Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…

Computer Vision and Pattern Recognition · Computer Science 2020-10-20 Pradyumna Reddy , Paul Guerrero , Matt Fisher , Wilmot Li , Miloy J. Mitra

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent,…

Dynamical Systems · Mathematics 2022-04-27 David W. Sroczynski , Felix P. Kemeth , Ronald R. Coifman , Ioannis G. Kevrekidis

This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…

Dynamical Systems · Mathematics 2024-06-05 Aleksandr Katrutsa , Ivan Oseledets , Sergey Utyuzhnikov

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…

Quantitative Methods · Quantitative Biology 2023-12-27 Steven A. Frank

What do data tell us about physics-and what don't they tell us? There has been a surge of interest in using machine learning models to discover governing physical laws such as differential equations from data, but current methods lack…

Machine Learning · Computer Science 2020-06-09 Steven Atkinson

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…

Optimization and Control · Mathematics 2026-04-28 Moad Abudia , Opeyemi Owolabi , Joel A. Rosenfeld , Rushikesh Kamalapurkar

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

Machine Learning · Statistics 2023-03-07 Sebastian Kaltenbach , Phaedon-Stelios Koutsourelakis , Petros Koumoutsakos

Discovering governing equations, whether manually or by data-driven methods, has been central in physics and related areas. Since governing equations are typically constrained by a set of symmetries, using symmetry constraints to restrict…

Statistical Mechanics · Physics 2026-04-03 Junya Yokokura , Kazumasa A. Takeuchi

We explore contemporary, data-driven techniques for solving math word problems over recent large-scale datasets. We show that well-tuned neural equation classifiers can outperform more sophisticated models such as sequence to sequence and…

Artificial Intelligence · Computer Science 2018-05-01 Benjamin Robaidek , Rik Koncel-Kedziorski , Hannaneh Hajishirzi

In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…

Machine Learning · Statistics 2023-11-03 Jinchao Feng , Charles Kulick , Sui Tang

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Machine Learning · Computer Science 2023-05-23 Yingtao Luo , Chang Xu , Yang Liu , Weiqing Liu , Shun Zheng , Jiang Bian

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large…

Machine Learning · Computer Science 2024-12-02 Parjanya Prashant , Ignavier Ng , Kun Zhang , Biwei Huang

Gradual argumentation frameworks represent arguments and their relationships in a weighted graph. Their graphical structure and intuitive semantics makes them a potentially interesting tool for interpretable machine learning. It has been…

Machine Learning · Computer Science 2021-06-28 Jonathan Spieler , Nico Potyka , Steffen Staab

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

Numerical Analysis · Mathematics 2024-05-02 Aviral Prakash , Yongjie Jessica Zhang

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Numerical Analysis · Mathematics 2024-04-04 Miha Rot , Martin Horvat , Gregor Kosec