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.
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.
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.
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.
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.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
Physics-informed deep learning for PDEs solves forward and inverse problems efficiently.
problem Solving forward and inverse problems in parametric PDEs efficiently and accurately.
method Physics-informed deep latent variable model (PDDLVM) combining deep neural networks, probabilistic modelling, and variational inference.
result Achieves up to three orders of magnitude speed-up compared to traditional FEM while providing coherent uncertainty estimates.
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.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
New method uses PINNs to solve complex PDEs with sparse measurements.
problem Joint estimation of source and parameters in advection-diffusion equations with limited data.
method Weighted adaptive approach based on neural tangent kernel of PINNs.
result Successful estimation of source function, velocity, and diffusion parameters.
PIED optimizes experimental design for inverse problems using physics-informed neural networks.
problem Optimizing experimental design for inverse problems with limited budget and constraints.
method PIED uses physics-informed neural networks (PINNs) for continuous optimization of design parameters in one-shot deployments.
result PIED significantly outperforms existing ED methods in solving inverse problems, including unknown functions.
Physics-informed GANs estimate elastic moduli from mechanical tests.
problem Estimating spatially-varying elastic moduli from measured deformations.
method Physics-informed Generative Adversarial Networks (PI-GANs) with PDE constraints.
result Generated stiffness samples match true distribution statistics.
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.
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.
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.
New model solves complex SDEs with high-dimensional spatial and stochastic spaces.
problem Solving SDEs with high-dimensional spatial and stochastic spaces.
method Physics-informed deep generative model (sPI-GeM) combining PI-BasisNet and PI-GeM.
result Scalable solution for high-dimensional SDE problems.
Proposes neural networks for solving complex free boundary problems.
problem Solving free boundary and Stefan problems with complex interfaces.
method Physics-informed neural networks for approximating solutions and boundaries.
result Successfully approximates solutions and moving boundaries in various Stefan problems.
New method uses machine learning to estimate drug parameters in brain models.
problem Estimating unknown parameters in complex brain drug models.
method Physics-Informed Neural Networks (PINNs) for inverse problem solving.
result Accurate parameter estimation leads to precise drug concentration profiles.
New model solves PDEs using probabilistic random grids.
problem Solving parametric PDEs with probabilistic collocation grids.
method Random Grid Neural Processes (RGNPs) with GICNets.
result Significant computational advantages and improved predictive capabilities.
PINNs solve neuronal parameter and state estimation problems with limited data.
problem Estimating parameters and hidden state variables from noisy partial data in multiscale neuronal models.
method Physics-informed neural networks (PINNs) for joint state and parameter estimation.
result PINNs deliver robust and accurate parameter inference and state reconstruction, even with limited data.
Develops a neural network approach to solve inverse stochastic problems from particle observations.
problem Inference of Fokker-Planck equation coefficients from sparse particle data.
method Physics-informed neural networks (PINNs) with Kullback-Leibler divergence loss.
result Simultaneous inference of Fokker-Planck equation and multi-dimensional PDF from few particle observations.
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
problem Detecting change-points and estimating parameters in nonlinear dynamical systems with regime transitions.
method Residual-loss anomaly analysis of physics-informed neural networks, two-stage strategy.
result The method outperforms traditional approaches in change-point localization and parameter estimation accuracy.
Bayesian PINN improves estimation of PDE solutions from noisy data.
problem Estimating solutions of PDEs from noisy measurements.
method Bayesian approach to Physics-informed neural networks (PINNs) for inverse problems.
result Convergence rate of Bayesian posterior mean error in PDE solutions.
Repulsive ensembles improve uncertainty estimates in PINNs for differential equations.
problem Improving uncertainty estimates in PINNs for differential equations.
method Employing repulsive ensembles (RE-PINN) with a repulsive term in the loss function.
result Repulsive ensembles produce more accurate uncertainty estimates and higher sample diversity.
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.
Bayesian PINNs solve noisy PDE problems with physics constraints.
problem Uncertainty quantification in noisy PDE problems.
method Bayesian framework combining PINNs and HMC/VI for posterior estimation.
result HMC outperforms VI for noisy data.
New PINN architectures learn high-frequency features using Fourier features.
problem PINNs struggle with high-frequency or multi-scale features.
method Employ spatio-temporal and multi-scale random Fourier features.
result Effective PINN models for multi-scale PDEs.
DeepONets combine neural networks with physics constraints for PDEs and parameter estimation.
problem Estimating parameters in PDEs with uncertainty quantification.
method Physics-informed neural networks (PINNs) integrated with Deep Operator Networks (DeepONets) for Bayesian inference.
result Robust and accurate solutions with comprehensive uncertainty quantification.
Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine lea…
This paper introduces VI for physics-informed deep learning, enhancing uncertainty quantification.
problem Uncertainty quantification in physics-informed deep learning.
method Variational inference for generative and inverse problems.
result VI provides a flexible and scalable approach for physics-based inference.
New method for efficient uncertainty quantification in DeepONets.
problem Efficient uncertainty quantification for DeepONets with limited and noisy data.
method Ensemble Kalman Inversion (EKI) for ensembles of DeepONets.
result Improved uncertainty estimates for DeepONet predictions.
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In particular, in addition to the deep neural network (DNN) for the solution, a second DNN …
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.
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
problem Reconstructing physical fields from limited and noisy data with known governing equations.
method Formalizing inverse problems via Bayesian inference in function spaces using a Brownian bridge Gaussian process.
result The Brownian bridge Gaussian process can be viewed as a physics-constrained prior for the Poisson equation, allowing for a fully Bayesian framework.
New method detects changepoints in PDEs using optimized neural networks.
problem Detecting changepoints in PDEs with unknown locations and times.
method Online optimized Physics-Informed Neural Networks (PINNs) with Total-Variation penalty.
result Improved parameter estimation and model fitting with changepoints.
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
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 method converts video of dye plumes into PDEs for better understanding.
problem Inferring continuum models from uncalibrated video data.
method Develops a pipeline to convert grayscale recordings into scalar fields, isolates drift, and identifies transport laws.
result Selected reduced model outperforms advection-diffusion baselines and retains structural interpretability.
New method solves high-dimensional Bayesian inverse problems efficiently.
problem Efficiently solving high-dimensional Bayesian inverse problems with limited data.
method Physics-informed Neural Operators with RealNVP architecture for invertibility and differentiability.
result Accurate approximations of the full posterior without additional forward solves or sampling.
This work combines machine learning with physical models to solve inverse problems efficiently.
problem Solving inverse problems in the presence of missing physics and recovering parameters.
method Variational autoencoding with a physically structured decoder network and stochastic local approximations.
result The method accelerates inference for Bayesian inverse problems and acts as a regularizer encoding prior physical information.
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.
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.
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.
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.
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.
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.
Paper explores physics-informed deep learning for system reliability assessment.
problem Limited study on deep learning for system reliability assessment.
method Physics-informed deep learning approach for system reliability assessment.
result Physics-informed deep learning can alleviate computational challenges and combine measurement data and mathematical models.
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.