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We focus on the control of unknown Partial Differential Equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a Reinforcement Learning framework. We…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources,…

We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergent space in which to learn predictive models in the form of…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

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…

Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…

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…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties.…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

In the fields of image restoration and image fusion, model-driven methods and data-driven methods are the two representative frameworks. However, both approaches have their respective advantages and disadvantages. The model-driven methods…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…