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Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided…

Machine Learning · Computer Science 2021-02-03 Suraj Pawar , Omer San , Burak Aksoylu , Adil Rasheed , Trond Kvamsdal

Two types of probabilistic maps are popular in the mobile robotics literature: occupancy grids and geometric maps. Occupancy grids have the advantages of simplicity and speed, but they represent only a restricted class of maps and they make…

Robotics · Computer Science 2012-07-09 Mark Paskin , Sebastian Thrun

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…

Artificial Intelligence · Computer Science 2025-07-15 Nathan Doumèche , Francis Bach , Gérard Biau , Claire Boyer

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

Machine Learning · Computer Science 2026-02-10 Maximilian Mauel , Johannes R. Hübers , David Berghaus , Patrick Seifner , Ramses J. Sanchez

Feature selection and regularization are becoming increasingly prominent tools in the efforts of the reinforcement learning (RL) community to expand the reach and applicability of RL. One approach to the problem of feature selection is to…

Machine Learning · Computer Science 2012-07-03 Christopher Painter-Wakefield , Ronald Parr

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

Disordered Systems and Neural Networks · Physics 2024-08-05 Takeru Yokota

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Machine Learning · Computer Science 2022-03-28 Alexander Henkes , Henning Wessels , Rolf Mahnken

The inductive bias of a neural network is largely determined by the architecture and the training algorithm. To achieve good generalization, how to effectively train a neural network is of great importance. We propose a novel orthogonal…

Machine Learning · Computer Science 2021-06-08 Weiyang Liu , Rongmei Lin , Zhen Liu , James M. Rehg , Liam Paull , Li Xiong , Le Song , Adrian Weller

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the…

Machine Learning · Computer Science 2025-10-28 Nima Hosseini Dashtbayaz , Hesam Salehipour , Adrian Butscher , Nigel Morris

We present a framework for solving time-dependent partial differential equations (PDEs) in the spirit of the random feature method. The numerical solution is constructed using a space-time partition of unity and random feature functions.…

Numerical Analysis · Mathematics 2023-04-17 Jingrun Chen , Weinan E , Yixin Luo

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Numerical Analysis · Mathematics 2025-07-10 Dimitrios Gazoulis , Ioannis Gkanis , Charalambos G. Makridakis

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

Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the…

Machine Learning · Statistics 2025-09-23 Nathan Doumèche , Francis Bach , Gérard Biau , Claire Boyer

The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so…

Materials Science · Physics 2021-11-22 Vadim V. Korolev , Yurii M. Nevolin , Thomas A. Manz , Pavel V. Protsenko

Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the…

Machine Learning · Computer Science 2018-02-19 Pengtao Xie , Wei Wu , Yichen Zhu , Eric P. Xing

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a…

Computer Vision and Pattern Recognition · Computer Science 2024-04-23 Maryam Haghighat , Peyman Moghadam , Shaheer Mohamed , Piotr Koniusz

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Machine Learning · Computer Science 2026-02-11 Davide Gallon , Philippe von Wurstemberger , Patrick Cheridito , Arnulf Jentzen

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Machine Learning · Computer Science 2023-11-30 Samuel Burbulla

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…

Machine Learning · Computer Science 2019-08-13 Grzegorz Dudek

We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…

Numerical Analysis · Mathematics 2025-05-20 Daniel Potts , Fabian Taubert