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.
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.
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.
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.
MetaPhysiCa tackles robust physics-informed machine learning for OOD tasks.
problem Designing robust PIML methods for OOD forecasting tasks in physics.
method Meta-learning procedure for causal structure discovery including invariant risk minimization.
result Significantly outperforms existing PIML and deep learning methods in OOD tasks.
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.
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.
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 GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
Unified physics-informed learning method improves generalization performance.
problem Lack of theoretical analysis for hybrid settings with incomplete physical constraints.
method Unified residual form unifying collocation and variational methods, establishing generalization performance governed by affine variety dimension.
result Generalization performance is determined by affine variety dimension, not just the number of parameters.
Paper develops error rates for physics-informed learning, comparing it to data-driven methods.
problem Understanding the trade-off between soft penalties and hard constraints in PISL.
method Develops complexity-dependent error rates using the small-ball method.
result Physics-informed estimators have comparable error rates to hard constrained methods, differing only by constants.
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.
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional lo…
Physics-informed WNO learns PDE solutions without labeled data.
problem Data-hungry nature of WNO framework.
method Physics-informed WNO for learning PDE solutions.
result Validated and illustrated with four nonlinear systems.
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 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.
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.
Physics-informed methods infer spatial dynamics from static snapshots, but limits exist.
problem Inferring spatial dynamics from static molecular patterns.
method Combining flexible representations with mechanistic constraints, analyzing structural identifiability, and adapting physics-informed schemes.
result Static spatial patterns can identify spatially varying dynamics, but limits exist due to modeling choices.
PIML uses physics equations in machine learning for better forecasting.
problem Forecasting time series data with physical constraints.
method Physics-informed neural networks (PINNs) and kernel methods.
result PIML improves forecasting accuracy with physical constraints.
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.
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
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.
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.
A new method for pricing European options in changing market conditions.
problem Lack of closed-form solutions for pricing European options in regime-switching models.
method Physics-informed residual learning (PIRL) for efficient option pricing.
result PIRL eliminates the need for retraining and offers near-instantaneous pricing.
Develops PAC-Bayesian framework for physics-informed machine learning.
problem Lack of statistical generalisation understanding for PIML models.
method PAC-Bayesian framework with multi-task perspective, incorporating physical structure.
result High-probability generalisation guarantees with unbounded losses.
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.
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.
DeepSVM learns SVMs without PDE solving, achieving high pricing accuracy.
problem Computational bottleneck in real-time calibration of stochastic volatility models.
method Physics-informed Deep Operator Network (PI-DeepONet) that enforces terminal payoffs and no-arbitrage conditions.
result DeepSVM achieves high pricing accuracy across various market dynamics.
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.
Survey of integrating physics knowledge into machine learning models.
problem Mitigating data shortage and ensuring physical plausibility.
method Combining physics knowledge with machine learning models.
result Summarizes recent works in physics-informed machine learning.
Physics-informed DeepONets solve PDEs without paired data, predicting solutions quickly.
problem Lack of paired input-output data for solving PDEs.
method Physics-informed DeepONets use automatic differentiation to enforce physical laws as soft penalty constraints.
result Physics-informed DeepONets can solve PDEs without paired data, predicting solutions up to 3 orders of magnitude faster.
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.
ξ-torch simplifies physics-informed learning by providing differentiable functionals.
problem Training physics-informed deep neural networks requires differentiable physical simulations.
method ξ-torch offers a library of differentiable functionals for scientific simulations.
result Improves numerical stability and reduces memory requirements for higher order derivatives.
This chapter reviews classic regression methods and their evolution to physics-informed approaches.
problem Finding relationships between variables using regression.
method Introduces traditional and physics-informed regression methods, linking them to computational science.
result Regression methods have evolved from purely statistical to incorporating physical knowledge.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
This work discovers governing equations from limited data using physics-informed deep learning.
problem Discovering governing equations from scarce and noisy data for complex systems.
method Physics-informed deep learning framework integrating neural networks, physics embedding, and sparse regression.
result The method effectively identifies governing equations from various spatiotemporal systems with different levels of data scarcity and noise.
Physics-guided reinforcement learning optimizes swimming in turbulent flows.
problem Optimizing swimming efforts to maintain proximity in turbulent environments.
method Physics-informed actor-physicist reinforcement learning algorithm.
result Physics-informed reinforcement learning outperforms standard methods in turbulent flow control.
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.
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.
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.
Improved method using filtered PDEs for robust physics-informed deep learning.
problem Complex real-world problems with noisy and sparse data.
method Proposed a surrogate constraint (FPDE) to filter and reduce the influence of noisy and sparse observation data.
result FPDE models converge better and produce higher quality solutions with less data.
GER learns particle dynamics from unpaired snapshots using physics-informed GANs.
problem Learning particle dynamics from unpaired snapshots with physics constraints.
method Physics-informed generative model to fit particle ensemble distributions.
result Inferred dynamics of particle ensembles governed by SODEs up to 100 dimensions.
This paper improves traffic flow modeling by using multi-gradient descent algorithms for physics-informed machine learning.
problem Combining physics-based and data-driven approaches in traffic flow modeling.
method Introducing multi-gradient descent algorithms to explore the Pareto front in a multi-objective setting.
result Multi-gradient descent algorithms significantly outperform scalarization-based methods in complex PIML scenarios.
PDE-NetGen converts physical equations to neural networks for various scientific problems.
problem Bridging physics and deep learning for efficient neural network architectures.
method Combines symbolic calculus and neural network generation to translate PDEs into NN architectures.
result Generates compact, computationally-efficient physics-informed NN architectures.
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).
PID-GAN uses physics knowledge to improve deep learning models' reliability.
problem Improving deep learning models' reliability in physics-based applications.
method Physics-informed GAN architecture that incorporates physics knowledge into both generator and discriminator models.
result PID-GAN framework outperforms state-of-the-art in handling gradient imbalance.
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.
Physics-informed deep learning approximates strain gradient plasticity solutions.
problem Stiffness and computational challenges in solving strain gradient plasticity models.
method Physics-informed deep learning (PIDL) with modified loss functions and optimization schemes.
result PIDL methods address stiffness and computational challenges in strain gradient plasticity.