Physics-informed GP regression solves eigenvalue problems by identifying non-trivial eigenspaces.
problem Solving eigenvalue problems of linear operators with trivial solutions.
method Constructing a transfer function-type indicator using physics-informed Gaussian Process posterior.
result The posterior covariance is non-trivial only for eigenvalues of the operator, indicating non-trivial eigenspaces.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
New GP model tackles physics constraints efficiently.
problem Lack of efficient, physics-informed models for complex systems.
method Physics-informed variational state-space Gaussian process.
result Efficient spatio-temporal modeling with improved performance.
Physics-informed model predicts beam stiffness and monitors structural health.
problem Predicting and monitoring the stiffness of Euler-Bernoulli beams.
method Physics-informed Gaussian process model using the Euler-Bernoulli beam equation.
result Model accurately predicts bending stiffness and detects structural damage.
In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters…
New score helps choose PIML model parameters, reducing ambiguity in model quality.
problem Ambiguity in measuring model quality in PIML due to multi-objective fitting.
method Introduces Physics-Informed Log Evidence (PILE) score in Gaussian process framework.
result PILE minimizes ambiguity in model selection, improving hyperparameter choices.
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 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.
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.
Gaussian Process Hydrodynamics approximates fluid flow equations using probabilistic kernels.
problem Approximating fluid flow equations with fewer particles and uncertainty estimates.
method Lagrangian particle-based approach with Gaussian Process (GP) prior and physics-informed kernels.
result GPH requires fewer particles and provides uncertainty estimates.
PAGP uses physics-assisted Gaussian processes to solve and learn PDEs.
problem Solving and discovering unknown coefficients in PDEs with initial and boundary conditions.
method Physics-assisted Gaussian processes with continuous, discrete, and hybrid models.
result Effective in solving and discovering unknown coefficients in PDEs.
DLFM models complex systems with uncertainty, outperforming traditional methods.
problem Modeling highly nonlinear dynamical systems with robust uncertainty quantification.
method Deep latent force model (DLFM) using physics-informed kernels derived from ODEs.
result DLFM achieves comparable performance to non-physics-informed models on univariate tasks and captures dynamics in real-world data.
PhI-GPR improves power grid state estimation and forecasting.
problem Accurate state estimation and forecasting in power grids with sparse measurements.
method Physics-informed Gaussian process regression (PhI-GPR) for stochastic differential equations.
result PhI-GPR provides more accurate forecasts and estimates of power grid states compared to ARIMA.
A novel model learns from limited data using physics constraints and GPVAE to generate realistic samples.
problem Limited data for effective generative AI training.
method Physics-informed Gaussian Process Variational Autoencoder (PIGPVAE) incorporating physical models and discrepancy terms.
result Achieves state-of-the-art performance on indoor temperature data.
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.
New method uses Gaussian processes to improve PDE solver accuracy.
problem Uncertainty in PDE solver parameters and measurements.
method Physics-informed Gaussian process regression.
result Strictly generalizes weighted residual methods.
Paper improves robustness of PINNs by smoothing and quantifying uncertainty.
problem PINNs can overfit and converge to local minima due to training data errors.
method Introduces Gaussian Process smoothing and sparse inducing points.
result Recover robust PINN performance against noise and errors.
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse accurate observation data are available. Specifically, the two types of multifi…
Machine learning reconstructs aerodynamic forces from noisy data.
problem Accurately modeling aerodynamic forces with limited or noisy data.
method Physics-informed Gaussian processes trained on noisy structural responses.
result Strong agreement between true and predicted aerodynamic loads.
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
Physics Informed Deep Kernel Learning improves prediction accuracy and uncertainty quantification.
problem Limited performance of deep kernel learning due to scarce or insufficient data.
method Integrates physics knowledge represented by differential equations with latent sources into deep kernel learning.
result Advantages in prediction accuracy and uncertainty quantification on synthetic and real-world datasets.
A new method uses multifidelity Gaussian process regression to solve nonlinear PDEs.
problem Efficiently solving nonlinear PDEs using kernel methods.
method Proposes a kernel learning approach based on cokriging for multifidelity simulations.
result Demonstrates improved performance on the Burgers' equation.
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…
PIMA autoencoders discover shared features in multimodal scientific data.
problem Discovering shared information in high-throughput scientific datasets.
method Physics-informed multimodal autoencoders (PIMA) with Gaussian mixture prior and product of experts formulation.
result Accurate cross-modal inference between images and mechanical stress-strain response in lattice metamaterials.
Quantum Gaussian processes enable scalable quantum learning.
problem Lack of simple, interpretable, scalable learning frameworks for quantum data.
method Bayesian framework using Gaussian processes with quantum kernels.
result Provable and scalable quantum Gaussian processes for quantum learning.
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.
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in…
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Paper introduces a method to learn physics between digital twins using imperfect models.
problem Learning physics from imperfect data and low-fidelity models.
method Bayesian Hierarchical modeling with physics-informed Gaussian processes.
result Models learning between digital twins are less uncertain than independent models but not over-confident.
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
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.
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.
Self-adaptive PINNs improve accuracy in stiff PDEs.
problem Accurate numerical solution of stiff PDEs using neural networks.
method Adaptive weights applied to each training point individually, using a soft attention mechanism.
result SA-PINNs outperform other PINN algorithms in L2 error with fewer training epochs.
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.
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
Paper proposes a dual-level approach for multi-step forecasting of dynamical systems.
problem Accurate multi-step forecasting of time series systems for automatic control and optimization.
method Hybrid input forecasting using LSTM-STMs and physics-informed neural networks (PINNs).
result Hybrid models achieve higher log-likelihood and lower MSE compared to conventional methods.
This work develops a machine learning approach to EOS models that accounts for thermodynamic constraints and model uncertainty.
problem Developing accurate equation of state models for high energy-density experiments with inherent uncertainties.
method Physics-informed Gaussian process regression (GPR) framework to capture model uncertainty and thermodynamic constraints.
result The proposed framework reduces prediction uncertainty by incorporating thermodynamic constraints, as demonstrated for diamond carbon EOS.
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.
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.
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.
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.
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.
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 novel score-based method solves high-dimensional Fokker-Planck equations with improved accuracy and speed.
problem High-dimensional Fokker-Planck equations suffer from the curse of dimensionality, leading to numerical errors and slow sampling.
method Score-based Physics-Informed Neural Networks (PINNs) that fit the score function in SDEs, using three methods: Score Matching, Sliced Score Matching, and Score-PINN.
result The score-based method outperforms traditional Monte Carlo and vanilla PINNs in high-dimensional settings, offering faster sampling and reduced errors.
We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements. Unlike standard GANs relying only on data for training, here we encoded into the architecture of GANs th…
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.
New neural network solves Nirenberg problem for curvature on sphere.
problem Prescribing Gaussian curvature on S2 for metrics conformal to the round metric. method Mesh-free physics-informed neural network (PINN) that directly parametrises the conformal factor.
result Neural network achieves very low losses for realisable curvatures, distinguishing them from non-realisable ones.