Researchers use GANs to infer physics-based inverse problems, quantifying uncertainty and promoting generalizability.
problem Quantifying uncertainty in physics-based inverse problems.
method Trained conditional Wasserstein GANs with U-Net architecture and conditional instance normalization.
result The approach effectively samples from the posterior and promotes generalizability with out-of-distribution samples.
We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural approach to this task, accompanied by a thorough experimental evaluation on a publicly …
Proposes ENOs for learning PDE solutions that conserve energy.
problem Learning dynamics that obey physical laws, especially in super-resolution settings.
method Energy-consistent Neural Operators (ENOs) with a novel penalty function inspired by energy-based theory.
result ENOs outperform existing DNN models in predicting solutions from data, especially in super-resolution settings.
Unified derivation of diffusion models using PDEs for inverse problems.
problem Solving inverse problems in physics-based applications.
method Deriving diffusion models using PDEs for a unified approach.
result Unified derivation and new class of variance preserving models.
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.
Enhances neural network solvers for PDEs with complex boundary conditions.
problem Challenges in solving PDEs with high accuracy and complex boundary conditions.
method Integrates natural gradient optimization with numerical time-stepping schemes to enforce Dirichlet boundary conditions.
result Superior accuracy and computational efficiency of the proposed methods for solving PDEs.
A new graph neural network framework captures long-range interactions efficiently.
problem Efficiently modeling long-range interactions in graph neural networks for PDEs.
method Proposes a multi-level graph neural network framework using multipole methods.
result Captures interaction at all ranges with only linear complexity, learning discretization-invariant solution operators.
This work surveys unsupervised learning methods for high-dimensional uncertainty quantification in complex PDEs.
problem Uncertainty quantification in high-dimensional stochastic inputs of complex PDEs.
method Review and investigation of thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods.
result Manifold PCE (m-PCE) provides a cost-effective approach compared to deep neural network-based surrogates.
We propose a physics-based method to learn environmental fields (EFs) using a mobile robot. Common purely data-driven methods require prohibitively many measurements to accurately learn such complex EFs. Alternatively, physics-based models provide global knowledge of EFs but require experimental validation, depend on u…
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
problem Lack of physical knowledge in black-box machine learning models.
method Embeds physics-based models into Gaussian Process mean function and uses kernel machines to characterize discrepancies.
result Improved model performance under blind conditions through integration of physics-based knowledge.
This paper introduces a framework for combining scientific knowledge of physics-based models with neural networks to advance scientific discovery. This framework, termed physics-guided neural networks (PGNN), leverages the output of physics-based model simulations along with observational features in a hybrid modeling …
PhICNet combines physics and deep learning for forecasting and source identification in dynamical systems.
problem Forecasting and identifying unobservable external sources in spatio-temporal dynamical systems.
method Physics-Incorporated Convolutional Recurrent Neural Network (PhICNet).
result PhICNet can forecast dynamics and identify sources for relatively long periods.
GINNs combine deep learning with PGMs for physics-based multiscale systems.
problem Intrinsic computational bottlenecks and lack of sufficient data for QoI estimation.
method Hybrid approach combining deep learning with probabilistic graphical models, informed by structured priors for CVs.
result GINNs produce tight confidence intervals for non-Gaussian QoIs.
PFPN uses particle filtering to improve character control in physics-based simulations.
problem Premature commitment to suboptimal actions in high-dimensional continuous control problems for articulated characters.
method Proposes a particle-based action policy using particle filtering to dynamically explore and discretize the action space.
result Demonstrates better imitation performance and robustness to external perturbations compared to Gaussian policies.
Physics-based framework improves building energy forecasting.
problem Lack of physical correspondence in machine learning models for building energy systems.
method Combines LTI SSMs with subspace-based domain adaptation (SDA).
result Physics-derived subspaces align with data-derived subspaces for better forecasting.
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
InVAErt networks use data-driven methods for system synthesis and identifiability analysis.
problem Model synthesis and identifiability analysis for complex systems.
method Deterministic encoder and decoder, normalizing flow, variational encoder, loss function penalty coefficients, latent space sampling.
result Validation through various system types, demonstrating effectiveness of the framework.
Machine learning in context of physical systems merits a re-examination of the learning strategy. In addition to data, one can leverage a vast library of physical prior models (e.g. kinematics, fluid flow, etc) to perform more robust inference. The nascent sub-field of \emph{physics-based learning} (PBL) studies the bl…
Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example faults not represented in training data, can be detected using, for example, ano…
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.
We enhance autonomous materials research with problem-aware models.
problem Complex decision-making in autonomous materials.
method Bayesian framework, machine learning, physics-based models, operational considerations.
result Improved models reflect problem-specific structure.
Physics-based deep learning improves fiber-optic communication efficiency.
problem Improving signal propagation in fiber-optic communication systems.
method Parameterizing the split-step method of solving the nonlinear Schrödinger equation as a deep neural network.
result Filters can be pruned to as few as 3 taps/step without sacrificing performance.
Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some information. We would ideally have a way to query the posterior probability of the enti…
Sig-PCA integrates model outputs and observations to correct model biases.
problem Improving model accuracy and reliability by correcting biases and numerical approximations.
method Sig-PCA framework that combines summary statistics from model outputs with localized observations via a neural network.
result Corrects model outputs to align closely with observational data, preserving essential statistical information.
Optimal sensor placement minimizes information loss from simulations.
problem Designing efficient sensor networks for spatiotemporal processes.
method Model-based sensor placement criterion with sparse variational inference and Gauss-Markov priors.
result Our method identifies sensor networks that minimize information loss from simulated data.
Hybrid model combines physics and data to handle incomplete systems.
problem Incomplete physics models with missing terms.
method Combines deep grey-box models with Optimal Transport.
result Enhances incomplete physics models with superior performance.
A digital twin for multi-scale systems uses physics-based and machine learning models.
problem Lack of application-specific details in digital twin technology.
method Strategically separates into physics-based and data-driven models; uses mixture of experts with Gaussian Process.
result Robust and accurate predictions at future time-steps for multi-scale systems.
In this paper, we present our approach to solve a physics-based reinforcement learning challenge "Learning to Run" with objective to train physiologically-based human model to navigate a complex obstacle course as quickly as possible. The environment is computationally expensive, has a high-dimensional continuous actio…
Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian …
Paper integrates ML with physics models for engineering and environmental challenges.
problem Complex science and engineering problems require new methodologies combining physics-based models and ML.
method Structured overview of integrating physics-based models with ML techniques.
result Taxonomy of existing techniques and potential research gaps identified.
In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs from physics-based models in learning a hybrid-physics-data model. Then, we furt…
A new method infers parameters from PDEs using Gaussian processes.
problem Estimating unknown parameters in PDEs from noisy data.
method PDE-Informed Gaussian Process (PIGP) method.
result The method bypasses numerical solvers for PDEs and provides uncertainty quantification.
Neural-PDE learns PDEs from data using LSTM, outperforming traditional methods.
problem Solving time-dependent PDEs numerically is challenging.
method Bidirectional LSTM encoder to learn governing rules from data.
result Neural-PDE efficiently predicts PDE dynamics with minimal parameters.
PIML model improves hydrological predictions by blending physics and ML.
problem Hydrological models either lack predictive accuracy or fail to maintain physical consistency.
method Physics Informed Machine Learning (PIML) that integrates physics-based models and ML algorithms.
result PIML model outperforms both physics-based and ML models in predicting streamflow and evapotranspiration.
New model learns better policies from expert demonstrations with higher efficiency.
problem Learning accurate policies from expert demonstrations with high efficiency.
method Generative adversarial imitation learning (GAIL) model that learns f-divergence automatically. result Learns better policies with higher data efficiency in physics-based control tasks.
Neural Q-learning tackles high-dimensional PDEs.
problem Solving high-dimensional PDEs is computationally challenging.
method Adapting Q-learning from reinforcement learning to solve PDEs.
result The neural network approximator converges to the PDE solution as the network width increases.
Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven discovery of PDEs. In this paper, we propose a new deep neural network, called PDE-Net …
A physics-based method improves data interpolators and regression tasks.
problem Improving accuracy and efficiency in function learning.
method Inspired by statistical mechanics, introduces corrections to minimize energy.
result Improves performance in interpolation and regression tasks, especially in high-dimensional spaces.
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties…
A deep learning approach solves probabilistic inverse problems with physical constraints.
problem Solving inverse problems with large inferred vectors and prior samples.
method Uses conditional Wasserstein generative adversarial networks (cWGAN) with full gradient penalty.
result Improves accuracy and robustness in sampling and solving inverse problems.
Solves second-order PDEs using quotients and differential invariants.
problem Solving second-order PDEs with first-order quotients.
method Solve the quotient PDE using differential invariants, then add new constraints to solve the original PDE.
result New method for solving second-order scalar PDEs with infinite-dimensional symmetry algebras.
PRISMA uses PDE residuals for fast, robust, and accurate inference.
problem Slow gradient-based optimization and instability in PDE residual-based methods.
method Integrates PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain.
result Competitive accuracy with significantly lower inference costs and faster speeds.
A deep neural network based architecture was constructed to predict amino acid side chain conformation with unprecedented accuracy. Amino acid side chain conformation prediction is essential for protein homology modeling and protein design. Current widely-adopted methods use physics-based energy functions to evaluate s…
Meta-learning base distributions for efficient PDE solutions.
problem Efficiently solving parametric parabolic PDEs across different scenarios.
method Meta-learning base distributions to compute PDE solutions.
result Improves generalization to new parameter regimes.
Kernel method learns PDEs from noisy data.
problem Discovering and solving PDEs from noisy data.
method Kernel smoothing, regression, and operator learning.
result Competitive performance compared to state-of-the-art algorithms.
Solves a PDE for Landsberg surfaces using new Finsler surface insights.
problem Solving the Landsberg's PDE for Finsler surfaces.
method Reduces the system of non-linear PDEs to a single PDE, the Landsberg's PDE, and solves it.
result Obtains a class of solutions for the Landsberg's PDE.
Survey on conservation laws for geometric PDEs.
problem Modeling polyharmonic maps.
method Conservation law approach.
result Overview of conservation laws in geometric PDEs.