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Found 48 papers, 34 papers with code
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces.
Understanding and mitigating gradient pathologies in physics-informed neural networks
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge.
Respecting causality is all you need for training physics-informed neural networks
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior.
Random Weight Factorization Improves the Training of Continuous Neural Representations
Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals.
An Expert's Guide to Training Physics-informed Neural Networks
Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints.
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks
While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and deeper neural network architectures are employed.
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training.
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features.
When and why PINNs fail to train: A neural tangent kernel perspective
In this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent.
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations
Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quantifying the uncertainty associated with such noisy data in our solutions to time-dependent partial differential equations.
$Δ$-PINNs: physics-informed neural networks on complex geometries
We approximate the eigenfunctions as well as the operators involved in the partial differential equations with finite elements.
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks.
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering.
Inferring solutions of differential equations using noisy multi-fidelity data
For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems.
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
Such models can be nowadays deployed on large patient-specific topologies of systemic arterial networks and return detailed predictions on flow patterns, wall shear stresses, and pulse wave propagation.
Long-time integration of parametric evolution equations with physics-informed DeepONets
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering.
Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data
This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems.
Bayesian differential programming for robust systems identification under uncertainty
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems.
Improved architectures and training algorithms for deep operator networks
In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel (NTK) theory, and reveal a bias that favors the approximation of functions with larger magnitudes.
Deep learning of free boundary and Stefan problems
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering.
Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models
In an application to cardiac electrophysiology, the multi-fidelity classifier achieves an F1 score, the harmonic mean of precision and recall, of 99. 6% compared to 74. 1% of a single-fidelity classifier when both are trained with 50 samples.
Fast PDE-constrained optimization via self-supervised operator learning
Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering.
Learning Operators with Coupled Attention
Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data.
Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems
We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems.
Semi-supervised Invertible Neural Operators for Bayesian Inverse Problems
Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces.
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks
We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation.
Analysis of PDEs Computational Physics
Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps
The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps.
PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems
We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk-planet interactions in protoplanetary disks in real-time.
Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors
Finally, we provide an optimized JAX library called {\em UQDeepONet} that can accommodate large model architectures, large ensemble sizes, as well as large data-sets with excellent parallel performance on accelerated hardware, thereby enabling uncertainty quantification for DeepONets in realistic large-scale applications.
Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling
In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points.
Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.
Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs
We present a new type of acquisition functions for online decision making in multi-armed and contextual bandit problems with extreme payoffs.
Machine Learning of Space-Fractional Differential Equations
We extend this framework to linear space-fractional differential equations.
Physics-informed deep generative models
We consider the application of deep generative models in propagating uncertainty through complex physical systems.
A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations
We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system.
Learning Unknown Physics of non-Newtonian Fluids
Once a viscosity model is learned, we use the PINN method to solve the momentum conservation equation for non-Newtonian fluid flow using only the boundary conditions.
Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks
In this work, we employ a recently developed approach, called physics informed neural networks, to learn the fiber orientations from electroanatomical maps, taking into account the physics of the electrical wave propagation.
Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization
Multilayer Perceptrons (MLPs) defines a fundamental model class that forms the backbone of many modern deep learning architectures.
Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification
Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites.
Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds
We propose a method for identifying an ectopic activation in the heart non-invasively.
NOMAD: Nonlinear Manifold Decoders for Operator Learning
Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling.
Variational Autoencoding Neural Operators
Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems.
Ensemble learning for Physics Informed Neural Networks: a Gradient Boosting approach
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems.
Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior
Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data.
Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex Geometries
By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain.
Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces.
