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Energy systems optimisation models are a leading tool for informing decisions in the energy transition. However, these models often remain opaque, and results are frequently presented without a clear discussion of their epistemic…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

Dynamical Systems · Mathematics 2020-10-19 Pipi Hu , Wuyue Yang , Yi Zhu , Liu Hong

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…

Machine Learning · Computer Science 2024-10-04 Doris Voina , Steven Brunton , J. Nathan Kutz

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Computational Physics · Physics 2019-10-31 Bing Xiong , Haiyang Fu , Feng Xu , Yaqiu Jin

Recent years have witnessed a surge in the development of protein foundation models, significantly improving performance in protein prediction and generative tasks ranging from 3D structure prediction and protein design to conformational…

Quantitative Methods · Quantitative Biology 2024-10-08 Fei Ye , Zaixiang Zheng , Dongyu Xue , Yuning Shen , Lihao Wang , Yiming Ma , Yan Wang , Xinyou Wang , Xiangxin Zhou , Quanquan Gu

Stance Detection (StD) aims to detect an author's stance towards a certain topic or claim and has become a key component in applications like fake news detection, claim validation, and argument search. However, while stance is easily…

Computation and Language · Computer Science 2020-01-07 Benjamin Schiller , Johannes Daxenberger , Iryna Gurevych

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

Machine Learning · Computer Science 2023-02-22 Alan A. Kaptanoglu , Lanyue Zhang , Zachary G. Nicolaou , Urban Fasel , Steven L. Brunton

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

Numerical Analysis · Mathematics 2020-11-10 Hassan Arbabi , Judith E. Bunder , Giovanni Samaey , Anthony J. Roberts , Ioannis G. Kevrekidis

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Methodology · Statistics 2022-09-08 Joshua S. North , Christopher K. Wikle , Erin M. Schliep

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

Numerical Analysis · Mathematics 2023-03-22 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

The Discovery Engine is a general purpose automated system for scientific discovery, which combines machine learning with state-of-the-art ML interpretability to enable rapid and robust scientific insight across diverse datasets. In this…

Existing benchmarks for computational materials discovery primarily evaluate static predictive tasks or isolated computational sub-tasks. While valuable, these evaluations neglect the inherently iterative and adaptive nature of scientific…

Machine Learning · Computer Science 2026-01-30 Shreshth A Malik , Tiarnan Doherty , Panagiotis Tigas , Muhammed Razzak , Stephen J. Roberts , Aron Walsh , Yarin Gal

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Numerical Analysis · Mathematics 2019-05-24 Omri Azencot , Wotao Yin , Andrea Bertozzi

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

Numerical Analysis · Mathematics 2007-06-21 Panagiotis Stinis

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Machine Learning · Computer Science 2022-09-21 Pratyush Bhatt , Yash Kumar , Azzeddine Soulaimani

Monocular Depth and Surface Normals Estimation (MDSNE) is crucial for tasks such as 3D reconstruction, autonomous navigation, and underwater exploration. Current methods rely either on discriminative models, which struggle with transparent…

Computer Vision and Pattern Recognition · Computer Science 2025-07-15 Alzayat Saleh , Melanie Olsen , Bouchra Senadji , Mostafa Rahimi Azghadi

Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…

Machine Learning · Statistics 2025-01-07 Debangshu Chowdhury , Souvik Chakraborty

Deep research, in which an agent searches the open web, collects evidence, and derives an answer through extended reasoning, is a prominent use case for frontier language models. Frontier deep research products score high on existing…

Artificial Intelligence · Computer Science 2026-05-21 Sixiong Xie , Zhuofan Shi , Haiyang Shen , Jiuzheng Wang , Siqi Zhong , Mugeng Liu , Chongyang Pan , Peilun Jia , Baoqing Sun , Xiang Jing , Yun Ma

Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…

Mathematical Software · Computer Science 2025-10-06 Arhonefe Joseph Ogethakpo , Ignatius Nkonyeasua Njoseh

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…

Methodology · Statistics 2025-07-10 Maren Hackenberg , Astrid Pechmann , Clemens Kreutz , Janbernd Kirschner , Harald Binder