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.
p3VAE combines physics and machine learning for robust data representations.
problem Improving machine learning models' robustness to environmental factors of variation.
method Physics-informed variational autoencoder integrating physical knowledge with neural networks.
result p3VAE outperforms competing models in extrapolation and interpretability. Develops VAEs for learning complex physical systems from data.
problem Learning low-dimensional representations of nonlinear physical systems.
method Variational Autoencoders with manifold latent spaces.
result Effective in learning nonlinear Burgers equation and constrained mechanical systems.
Proposes a physics-informed VAE for disentangling physics from confounding influences.
problem Challenges in inferring and predicting physical systems under partial knowledge.
method Physics-informed variational autoencoder with adversarial training.
result Model successfully disentangles known physics from confounding influences.
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.
We develop VAE-DLM for dynamics with geometric flows in latent space.
problem Learning latent geometric properties for dynamics in high-dimensional data.
method Riemannian approaches to VAEs with a geometric flow in latent space, reformulating ELBO loss.
result Improved performance and robust learning for external dynamics, reducing OOD error.
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.
Develops Φ-DVAE for assimilating unstructured data into physical models.
problem Challenges in incorporating unstructured data into physical models.
method Physics-informed dynamical variational autoencoder (Φ-DVAE) combining latent state-space model and VAE. result Demonstrates data-efficient dynamics encoding with competitive performance and uncertainty quantification.
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.
Paper uses VAEs to model yield curves without arbitrage violations.
problem Forecasting yield curves across diverse macroeconomic regimes leads to arbitrage violations.
method Proposes a two-stage architecture with CVAEsT+LS and Neural SDEs penalized by No-Arbitrage PDE.
result Significantly reduces forecasting errors and overcomes HJM model limitations.
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.
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 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.
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 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.
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…
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.
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.
In this paper, we integrate VAEs and flow-based generative models successfully and get f-VAEs. Compared with VAEs, f-VAEs generate more vivid images, solved the blurred-image problem of VAEs. Compared with flow-based models such as Glow, f-VAE is more lightweight and converges faster, achieving the same performance und…
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.
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.
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.
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 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.
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.
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 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.
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 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.
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.
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.
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.
This work tackles posterior collapse in conditional and hierarchical VAEs.
problem Posterior collapse in VAEs leads to poor latent variable representations.
method Theoretical analysis of linear conditional and hierarchical VAEs, empirical validation.
result Theoretical and empirical evidence of posterior collapse causes in conditional and hierarchical VAEs.
BS-VAE separates decoder variance and beta to improve VAE performance.
problem Blurriness in VAE outputs and difficulty in analyzing model performance.
method Explicitly separates beta and decoder variance in Beta-Sigma VAE.
result Superior performance in natural image synthesis and controllable parameters.
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.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
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.
Physics-informed diffusion model detects anomalous trajectories in GPS data.
problem Detecting fake GPS trajectories in international waters.
method Physics-informed diffusion model integrating kinematic constraints.
result Higher prediction accuracy and lower error rate for anomaly detection.
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.
A tutorial on VAEs explaining its derivation and applications.
problem Understanding the VAE model and its limitations.
method Explains VAE through probabilistic and information theoretic perspectives.
result Identifies two common misconceptions and their practical consequences.
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.
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.
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 system for i-vector speaker recognition based on variational autoencoder (VAE) is investigated. VAE is a promising approach for developing accurate deep nonlinear generative models of complex data. Experiments show that VAE provides speaker embedding and can be effectively trained in an unsupervised manner. LLR est…
The paper provides convergence guarantees for VAEs using SGD and Adam.
problem Understanding theoretical convergence guarantees for VAEs.
method Derives non-asymptotic convergence rates for VAEs trained with SGD and Adam.
result Convergence rate of \(\mathcal{O}(\log n / \sqrt{n})\) with explicit hyperparameter dependencies.
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.
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.