Related papers: Physics informed operator learning of parameter de…

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…

Reliability analysis of engineering systems under uncertainty poses significant computational challenges, particularly for problems involving high-dimensional stochastic inputs, nonlinear system responses, and multiphysics couplings.…

Spectral bias, the tendency of neural networks to prioritize learning low-frequency components of functions during the initial training stages, poses a significant challenge when approximating solutions with high-frequency details. This…

Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining…

Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…

Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…

Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based…

Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of…

We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for…

We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…

The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…

Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…

A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…

Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…