Related papers: Generative Models for Parameter Space Reduction ap…
In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…
In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance…
Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…
Heralded by the initial success in speech recognition and image classification, learning-based approaches with neural networks, commonly referred to as deep learning, have spread across various fields. A primitive form of a neural network…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
SGM-PINN is a graph-based importance sampling framework to improve the training efficacy of Physics-Informed Neural Networks (PINNs) on parameterized problems. By applying a graph decomposition scheme to an undirected Probabilistic…
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…
We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…
Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative…
Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…
Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…