Related papers: Hidden Physics Models: Machine Learning of Nonline…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

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…

We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest…

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled.…

We present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system's governing equations to identify a coordinate transformation in which the…