Adaptive weights improve physics-informed neural networks and deep operator networks.
problem Training physics-informed neural networks and deep operator networks can be challenging, leading to unsatisfactory accuracy and efficiency.
method Proposes a pointwise adaptive weighting method that balances the residual decay rate across different training points.
result Our proposed approach of balanced residual decay rates offers advantages including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.
Physics-informed neural networks improve pathloss prediction accuracy.
problem Improving pathloss prediction accuracy in wireless communications.
method Physics-informed neural networks incorporating physical dependencies and measured values.
result Physics-informed neural networks achieve better generalization and prediction quality with fewer layers and parameters.
New DDMs use neural networks for solving equations on manifold shapes.
problem Solving equations on complex, high-dimensional shapes.
method Physics-informed neural networks combined with domain decomposition methods.
result Validated methods work well on various shapes in high dimensions.
New method solves PDEs on spheres using physics-informed convolutional neural networks.
problem Solving PDEs on surfaces, especially spheres, with high accuracy and efficiency.
method Physics-informed convolutional neural networks (PICNN) with theoretical analysis and approximation results.
result Established fast convergence rates for PICNN solving PDEs on spheres.
jinns is a JAX library for physics-informed neural networks.
problem Physics-informed neural networks for forward and inverse problems.
method Physics-informed neural networks using JAX ecosystem.
result Efficient prototyping and extensions for real problems.
Physics-informed neural networks simulate radiative transfer efficiently.
problem Simulating radiative transfer accurately and efficiently.
method Physics-informed neural networks trained to minimize radiative transfer equations.
result PINNs provide an easy-to-implement, robust, and accurate method for radiative transfer simulation.
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
PICN learns physical fields from shallow neural networks, improving AI in multi-physical systems.
problem Challenges in modeling and forecasting multi-physical systems due to data scarcity and noise.
method Physics-informed convolutional network (PICN) combining CNN and physical laws, using deconvolution and convolution layers.
result PICN effectively solves and estimates nonlinear physical operator equations and recovers physical information from noisy observations.
Physics-Informed Neural Network improves option pricing accuracy.
problem Improving option pricing accuracy using machine learning.
method Physics-Informed Neural Network (PINN) applied to Black-Scholes equation.
result PINN model accurately captures option pricing behavior on both simulated and real market data.
Enhances physics-informed neural networks with adaptive sampling and weighting.
problem Challenges in training physics-informed neural networks on complex problems.
method Hybrid adaptive sampling and weighting method.
result Consistently improves prediction accuracy and training efficiency.
Paper develops a new model for predicting volatility surface.
problem Predicting volatility in financial markets is challenging due to its non-observable nature and complex dynamics.
method Physics-informed convolutional transformer architecture.
result The new model outperforms other deep-learning architectures in predicting volatility surface.
PD-PINNs accelerate PINN training by incorporating task-specific dictionaries.
problem Training PINNs is slow and lacks theoretical error bounds.
method Integrates task-dependent dictionaries into PINNs to enhance convergence.
result PD-PINNs achieve faster convergence and bounded prediction errors.
A new method uses physics-informed neural networks to solve reliability analysis problems without simulations.
problem Solving reliability analysis problems without the need for expensive simulations.
method Physics-informed neural networks to learn directly from problem physics.
result Eliminates the need for expensive simulations and achieves highly accurate results.
Unified bounds for neural networks incorporating physical laws.
problem Limitations in existing generalization analyses for PINNs and VPINNs.
method Unified framework using Taylor expansion and Koopman-based analysis.
result High-rank networks can generalize well even with differential operators.
Physics-informed neural networks improve baryonic predictions from dark matter simulations.
problem Recreating hydrodynamic simulations from dark matter requires expensive and time-consuming computations.
method Combining neural network architectures with physical constraints and using Kullback-Leibler divergence for prediction comparison.
result Improved accuracy of baryonic predictions based on dark matter halo properties, successful recovery of the metallicity relation, and preserved scatter.
Paper discovers differential equations from data using neural networks and Bayesian methods.
problem Discovering differential equations from datasets using machine learning.
method Integrates neural network-based surrogates with Sparse Bayesian Learning (SBL).
result Proposes a robust model discovery algorithm and a Physics Informed Normalizing Flow (PINF).
Improved PINNs for solving PDEs with unknown measurement noise.
problem Handling non-Gaussian noise in physics-informed neural networks.
method Jointly train an EBM to learn the correct noise distribution.
result Improved performance in solving PDEs with non-Gaussian noise.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Paper improves uncertainty quantification in PINNs using error bounds and solution bundles.
problem Uncertainty quantification in PINNs for differential equation systems.
method Two-step procedure with Bayesian Neural Networks and heteroscedastic variance.
result Improved uncertainty estimation over PINNs solutions in differential equation systems.
Physics-informed kernel learning integrates physical priors into machine learning models.
problem Tackles the integration of physical laws into machine learning models for improved accuracy and efficiency.
method Uses Fourier methods to approximate the kernel and minimizes a physics-informed risk function.
result Demonstrates PIKL outperforms physics-informed neural networks and traditional PDE solvers in various scenarios.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
problem Calculating the Gerber-Shiu function efficiently.
method Physics-informed neural networks (PINNs) embedded with differential equations.
result Demonstrates good performance in approximating Gerber-Shiu functions.
New method uses EKI for efficient Bayesian inference in high-dimensional problems.
problem Efficient inference for high-dimensional posterior distributions in physics-informed neural networks.
method Ensemble Kalman Inversion (EKI) for high-dimensional posterior inference.
result EKI-based inference provides comparable uncertainty estimates to HMC-based methods but with reduced computational cost.
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the em…
Physics-informed neural networks and neural operators speed up solving parametric PDEs by orders of magnitude.
problem Solving PDEs for varying parameters is computationally expensive.
method Physics-informed neural networks and neural operators learn solution mappings across parameter spaces.
result Neural operators achieve computational speedups of 10^3 to 10^5 times faster than traditional methods.
Meta-learning neural networks to solve diverse PDEs efficiently.
problem Efficiently solving new PDE problems with minimal training.
method Neural network meta-learning of PDE problem representations.
result Meta-learned neural networks predict PDE solutions with high accuracy.
Physics-informed neural networks improve model accuracy and efficiency.
problem Accurate dynamic models for technical systems are hard to achieve.
method Physics-informed neural ordinary differential equations (PINODE) integrating Lagrangian mechanics.
result Hybrid model combines physical insight and data approximation.
Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.
problem Solving partial differential equations on complex geometries with physics constraints.
method Combines admissible NURBS parametrizations and PINN solver for arbitrary geometries.
result High convergence rate and accuracy for most PDEs using Deep NURBS.
Paper presents MF-PIDNN for physics-informed deep learning with low-fidelity data.
problem Challenges in systems with unknown or approximate governing differential equations and limited high-fidelity data.
method Transfer learning between physics-informed and data-driven deep learning models.
result Model provides accurate predictions even in data-scarce regions.
Bayesian PINNs optimize loss weights for PDEs and data.
problem Optimizing loss weights in physics-informed neural networks.
method Laplace approximation for efficient model evidence computation.
result Unified Bayesian setting for PDEs and noisy measurements.
Proposes PI-VAE for solving SDEs with limited measurements.
problem Solving SDEs with limited measurements of system parameters.
method Physics-informed Variational Autoencoder (PI-VAE) integrating VAE and governing equations.
result Satisfactory accuracy and efficiency compared to PI-WGAN.
Physics-informed neural network identifies and characterizes surface cracks in metals.
problem Identifying and characterizing surface-breaking cracks in metals using ultrasound.
method Physics-informed neural network (PINN) trained with ultrasonic surface wave data and adaptive activation functions.
result PINN accurately estimates the speed of sound and identifies crack locations in metals.
APINNs use neural networks to solve MCMC problems efficiently.
problem Accurate Bayesian parameter estimation for systems governed by PDEs.
method Construct an offline PINN-UQ model and refine it on the fly using MCMC samples.
result Guaranteed approximation error less than a residual error threshold.
PINNs struggle with increasingly complex ODEs, especially when parameters control their complexity.
problem Evaluating physics-informed neural networks on complex coupled ODEs.
method Tuned benchmarks of partial differential equations and harmonic oscillators; varying network architecture and training method.
result PINNs fail to solve complex ODEs, revealing issues like insufficient capacity, poor conditioning, and high local curvature.
This study compares different thermodynamic structure-informed neural networks for solving differential equations.
problem Improving the accuracy and physical consistency of neural network solutions to differential equations.
method Comprehensive evaluation of various thermodynamic formulations in physics-informed neural networks.
result Newtonian-residual-based PINNs fail to reliably recover physical quantities, while structure-preserving formulations enhance accuracy and robustness.
Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically-consistent deep neural network architectures is an open issue. In the spirit of physics-informed NNs, PDE-NetGen package provides new means to automatically translate phys…
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. In this two part treatise, we present our developments in the context of solving two main classes …
Paper improves training physics-informed neural networks with model ensembles.
problem Training physics-informed neural networks (PINNs) is difficult due to convergence to wrong solutions.
method Proposes training an ensemble of PINNs, using ensemble agreement to expand the solution interval.
result Algorithm stabilizes PINN training and yields competitive performance.
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neur…
New framework explains neural network bias in solving differential equations.
problem Understanding and controlling the bias in PINNs for differential equations.
method Deriving an integro-differential equation from PINNs and GPR equivalence.
result PINN predictions are influenced by a kernel term reflecting architecture choices.
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed Extreme Learning Machine (PIELM), a rapid version of PINNs which can be applied to s…
Physics-informed machine learning models improve biomolecular system simulations.
problem Modeling unresolved interactions beyond classical force fields.
method Physics-informed neural networks and operator learning.
result Accurate, mechanistic, generalizable models for long-timescale kinetics.
This study evaluates the importance of design of experiments for PINN in physics-informed deep learning.
problem Accuracy of PINN predictions depends on the design of experiment scheme.
method Comparative study of five PDEs using different design of experiment schemes.
result Hammersley sampling-based PINN outperforms other design of experiment schemes.
Score-fPINN tackles high-dimensional FPL equations using fractional score functions.
problem High-dimensional Fokker-Planck-Lévy equations with non-Brownian processes.
method Fractional score function and Physics-informed neural networks (PINN) to solve CoD and numerical overflow.
result Effective solution to high-dimensional FPL equations without fractional Laplacian.
This article introduces machine learning methods for solving PDEs.
problem Approximating solutions of partial differential equations.
method Machine learning methods, including physics-informed neural networks and deep operator learning.
result Recent advances in machine learning have made PDE solutions more accessible.
Unified Bayesian PINN framework for solving inverse problems in infrared image processing.
problem Solving inverse problems in high-dimensional settings with complex physics.
method Bayesian Physics-Informed Neural Networks (BPINN-IP) framework, incorporating physical laws and uncertainties.
result Unified framework for physical constraints, prior knowledge, and data-driven inference with uncertainty quantification.
APINNs improve physics-informed neural networks through flexible domain decomposition.
problem Improving physics-informed neural networks (PINNs) for solving partial differential equations (PDEs).
method Introduces a trainable gate network for soft domain decomposition, allowing flexible parameter sharing and improved generalization.
result APINNs significantly improve PINNs and XPINNs, demonstrating better performance on various types of PDEs.
INEUS solves high-dimensional PIDEs efficiently with neural networks.
problem Solving high-dimensional partial integro-differential equations (PIDEs) efficiently.
method INEUS uses iterative neural networks to replace nonlocal integrals with sampling and reformulates PIDE solving as recursive regression.
result INEUS delivers accurate and scalable solutions for high-dimensional linear and nonlinear PIDEs.
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.