Related papers: Physics-informed deep learning for flow and deform…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…

We report the application of machine learning methods for predicting the effective diffusivity (De) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as…

We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy…

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts…

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables…

The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…

A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…

We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…

Recently, computational modeling has shifted towards the use of deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by…

Physics-informed neural networks have emerged as a coherent framework for building predictive models that combine statistical patterns with domain knowledge. The underlying notion is to enrich the optimization loss function with known…

We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with…

The present study investigates the accurate inference of Reynolds-averaged Navier-Stokes solutions for the compressible flow over aerofoils in two dimensions with a deep neural network. Our approach yields networks that learn to generate…

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…

Existing point cloud representation learning methods primarily rely on data-driven strategies to extract geometric information from large amounts of scattered data. However, most methods focus solely on the spatial distribution features of…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…