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Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

Machine Learning · Computer Science 2025-03-26 Amin Totounferoush , Serge Kotchourko , Michael W. Mahoney , Steffen Staab

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Machine Learning · Computer Science 2025-02-11 Elisa Negrini , Yuxuan Liu , Liu Yang , Stanley J. Osher , Hayden Schaeffer

Reinforcement learning techniques achieved human-level performance in several tasks in the last decade. However, in recent years, the need for interpretability emerged: we want to be able to understand how a system works and the reasons…

Machine Learning · Computer Science 2023-01-13 Leonardo Lucio Custode , Giovanni Iacca

Recently, many evolutionary computation methods have been developed to solve the feature selection problem. However, the studies focused mainly on small-scale issues, resulting in stagnation issues in local optima and numerical instability…

Neural and Evolutionary Computing · Computer Science 2021-10-28 Xubin Wang , Yunhe Wang , Ka-Chun Wong , Xiangtao Li

Acquiring abilities in the absence of a task-oriented reward function is at the frontier of reinforcement learning research. This problem has been studied through the lens of empowerment, which draws a connection between option discovery…

Machine Learning · Computer Science 2020-08-04 Víctor Campos , Alexander Trott , Caiming Xiong , Richard Socher , Xavier Giro-i-Nieto , Jordi Torres

Electrocardiogram (ECG) signals, which capture the heart's electrical activity, are used to diagnose and monitor cardiac problems. The accurate classification of ECG signals, particularly for distinguishing among various types of…

EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel approach at the intersection of machine learning and dynamical systems theory, presenting a unique framework for classification tasks [1]. This…

Machine Learning · Computer Science 2024-05-21 Raffaele Marino , Lorenzo Buffoni , Lorenzo Chicchi , Lorenzo Giambagli , Duccio Fanelli

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

Numerical Analysis · Mathematics 2024-09-05 Xiaodong Feng , Haojiong Shangguan , Tao Tang , Xiaoliang Wan , Tao Zhou

Differential Evolution (DE) is a renowned optimization stratagem that can easily solve nonlinear and comprehensive problems. DE is a well known and uncomplicated population based probabilistic approach for comprehensive optimization. It has…

Neural and Evolutionary Computing · Computer Science 2015-06-22 Sandeep Kumar , Vivek Kumar Sharma , Rajani Kumari

Most of the real-world problems are multimodal in nature that consists of multiple optimum values. Multimodal optimization is defined as the process of finding multiple global and local optima (as opposed to a single solution) of a…

Neural and Evolutionary Computing · Computer Science 2022-08-24 Shatendra Singh , Aruna Tiwari

Document-level relation extraction (DocRE) aims to extract semantic relations among entity pairs in a document. Typical DocRE methods blindly take the full document as input, while a subset of the sentences in the document, noted as the…

Computation and Language · Computer Science 2022-03-08 Yiqing Xie , Jiaming Shen , Sha Li , Yuning Mao , Jiawei Han

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

Machine Learning · Computer Science 2023-05-29 Yingtao Luo , Qiang Liu , Yuntian Chen , Wenbo Hu , Tian Tian , Jun Zhu

Accurate screening of cancer types is crucial for effective cancer detection and precise treatment selection. However, the association between gene expression profiles and tumors is often limited to a small number of biomarker genes. While…

Neural and Evolutionary Computing · Computer Science 2024-04-09 Xubin Wang , Yunhe Wang , Zhiqing Ma , Ka-Chun Wong , Xiangtao Li

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

Machine Learning · Computer Science 2019-10-24 Ali Hasan , João M. Pereira , Robert Ravier , Sina Farsiu , Vahid Tarokh

This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…

Machine Learning · Statistics 2023-04-03 Da Long , Nicole Mrvaljevic , Shandian Zhe , Bamdad Hosseini

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Pattern Formation and Solitons · Physics 2025-06-06 Shaoxuan Chen , Su Yang , Panayotis G. Kevrekidis , Wei Zhu

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

Machine Learning · Computer Science 2025-11-04 G. Pillonetto , A. Giaretta , A. Aravkin , M. Bisiacco , T. Elston

LLM-based equation discovery offers a promising route to recovering symbolic laws from data, but many systems still rely on generation-centered loops that propose candidates, fit parameters, score results, and reuse selected examples. Such…

Artificial Intelligence · Computer Science 2026-05-19 Jiarui Su , Songjun Tu , Bei Sun , Xiaojun Liang

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…

Machine Learning · Computer Science 2022-12-09 Rajat Arora , Ankit Shrivastava

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

Machine Learning · Computer Science 2026-05-21 Jianhong Chen , Naichen Shi , Xubo Yue