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We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Machine Learning · Statistics 2023-10-23 Tomoharu Iwata , Yusuke Tanaka , Naonori Ueda

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Machine Learning · Computer Science 2023-04-12 Aleksandr Dekhovich , Marcel H. F. Sluiter , David M. J. Tax , Miguel A. Bessa

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm…

Machine Learning · Computer Science 2024-03-27 Zhiwei Fang , Sifan Wang , Paris Perdikaris

This work concerns the application of physics-informed neural networks to the modeling and control of complex robotic systems. Achieving this goal required extending Physics Informed Neural Networks to handle non-conservative effects. We…

Robotics · Computer Science 2023-07-07 Jingyue Liu , Pablo Borja , Cosimo Della Santina

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…

Systems and Control · Electrical Eng. & Systems 2023-11-13 Jochen Stiasny , Spyros Chatzivasileiadis

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Quantum Physics · Physics 2026-04-17 Nils Klement , Veronika Eyring , Mierk Schwabe

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…

Optimization and Control · Mathematics 2025-02-06 Christoph Plate , Mirko Hahn , Alexander Klimek , Caroline Ganzer , Kai Sundmacher , Sebastian Sager

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

The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…

Systems and Control · Electrical Eng. & Systems 2025-10-08 Ignasi Ventura Nadal , Rahul Nellikkath , Spyros Chatzivasileiadis

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

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…

Machine Learning · Computer Science 2018-11-22 Bryan Wilder , Bistra Dilkina , Milind Tambe

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Numerical Analysis · Mathematics 2024-11-20 Tim De Ryck , Siddhartha Mishra

Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Yiming Meng , Ruikun Zhou , Amartya Mukherjee , Maxwell Fitzsimmons , Christopher Song , Jun Liu

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a…

Computational Physics · Physics 2019-02-01 Xiaowei Jia , Jared Willard , Anuj Karpatne , Jordan Read , Jacob Zwart , Michael Steinbach , Vipin Kumar

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

Optimization and Control · Mathematics 2021-10-22 Calvin Tsay , Jan Kronqvist , Alexander Thebelt , Ruth Misener

The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

Machine Learning · Computer Science 2022-09-09 Danial Amini , Ehsan Haghighat , Ruben Juanes

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

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

Machine Learning · Computer Science 2024-02-13 Hao Chen , Gonzalo E. Constante Flores , Can Li

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