Despite the wide implementation of machine learning (ML) techniques in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PR…
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48 results for “physics regularization”
Physics-enhanced NNs improve predictive accuracy in small data scenarios.
problem Predicting physical systems dynamics with limited data.
method Integrating physical principles (Hamiltonian/Lagrangian) and regularization term based on energy level into neural networks.
result Significant gains in predictive accuracy for small data cases.
New PRGP model improves traffic flow estimation.
problem Lack of models combining physics and ML for traffic flow.
method Physics regularized Gaussian process (PRGP) with discrete formulations.
result PRGP model outperforms calibrated physics models and ML methods.
Physics-Driven Regularization of Deep Neural Networks for Enhanced Engineering Design and Analysiscs.LG
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in addition to training data, partial or complete information on a set of governing la…
The author exposes the metrical multi-time Lagrange geometry of physical fields which naturally generalizes the classical Lagrangian developped by Miron and Anastasiei. In other words, one constructs a natural theory of physical fields on the 1-jet fibre bundle, attached to a Kronecker h-regular multi-time Lagrangian w…
Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approachstat.ML
A new model captures car-following and lane-changing behaviors in traffic.
problem Modeling stochastic microscopic traffic behaviors.
method Physics regularized Gaussian process (PRGP) approach.
result The proposed model outperforms previous methods in estimation precision.
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations. Such physics…
Gibbs pruning optimizes neural networks by combining physics and regularization.
problem Large neural networks are impractical for many applications.
method Combines statistical physics and stochastic regularization to train and prune networks simultaneously.
result Gibbs pruning achieves state-of-the-art performance on ResNet-56.
VED framework learns low-dimensional latent representations of physical systems.
problem Learning latent representations of complex physical systems.
method Variational Encoder-Decoder (VED) framework with KL divergence and covariance regularization.
result VED achieves lower-dimensional latent representations with improved feature disentanglement.
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.
Proposes volumization for neural networks to control bias-variance tradeoff.
problem Improving generalization and preventing memorization in neural networks.
method Defines a physical volume for weights, interpolating between L2 and L∞ regularization.
result Volumization interpolates between weight decay and clipping, improving generalization.
We propose weight-sharing regularization for neural networks.
problem Training fully connected networks with shuffled pixel data.
method Introduce a regularization penalty on weights and design parallel algorithms.
result Weight-sharing regularization enables learning convolution-like filters.
The limits of interpretability in multiple linear regressioncond-mat.dis-nn
Interpretable machine-learning models can be unstable under multicollinearity, leading to oscillatory weights that do not reflect meaningful contributions.
problem Interpretable machine-learning models can be unstable under multicollinearity.
method Theoretical analysis of eigenmodes of the feature correlation matrix.
result Small-eigenvalue modes associated with multicollinearity amplify fluctuations in the weights and generate oscillatory patterns that do not necessarily reflect meaningful contributions.
Paper connects RL and non-equilibrium statistical mechanics for entropy-regularized RL.
problem Obtaining analytical solutions for entropy-regularized RL.
method Mapping RL to non-equilibrium statistical mechanics, applying large deviation theory.
result Derives exact analytical results for optimal policy and dynamics in MDPs.
We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.
Physics models integrated into VAEs improve generative performance and extrapolation.
problem Improving generative models with interpretability and robustness.
method Physics-based latent space in VAEs with regularized learning to balance physics and neural network components.
result Generative performance and extrapolation improvements demonstrated on synthetic and real-world datasets.
New method identifies physical constants from video data alone.
problem Identifying physical constants from video data.
method Proves level-set slope-coverage condition ensures local affine mapping to true physical state, enabling exact parameter recovery.
result Underdamped systems identifiable from a single video clip, other regimes require three diverse trajectories.
Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Biasstat.ML
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.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
FunDiff models physical functions using diffusion and autoencoders.
problem Adapting generative models to continuous physical functions.
method Combines latent diffusion with function autoencoder, enforcing physical priors.
result Achieves optimal convergence rates for physical function estimation.
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial …
Transformer-based multi-scale model outperforms traditional methods in solving PDEs on irregular domains.
problem Solving partial differential equations on irregular domains using deep learning.
method Introduces Multi-Scale Attention Transformer (\msat{}) for solving PDEs.
result Achieves state-of-the-art generalization on complex geometry problems with significant speedup.
Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Methodstat.ML
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.
Data coarse graining can improve model performancecond-mat.stat-mech
Data coarse graining improves model performance by filtering out less relevant features.
problem Lossy data transformations lose information but can improve model generalization.
method Data coarse graining schemes that systematically discard features based on relevance to the learning task.
result A 'high-pass' scheme helps models generalize better by filtering out less relevant features.
MUSIC learns coupled systems with sparse data and incomplete physics.
problem Learning coupled systems with incomplete physical constraints and missing data.
method Sparsity induced multitask neural network framework integrating partial physical constraints with data-driven learning.
result MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions.
Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable due to system dynamics and uncertainties, making traditional numerical approach…
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 regression analysis using Padé approximants with new residuals and regularization.
problem Improving regression analysis with Padé approximants for accuracy and avoiding overfitting.
method New residuals in least squares method, system of linear equations for rational functions, Tikhonov regularization.
result Demonstrated efficiency in practical cases from physics and reliability theory.
Efficient algorithm for mobile health provides timely physical activity suggestions.
problem Inefficient reinforcement learning for mobile health settings.
method Contextual bandit algorithm with linear mixed effects model and hyper-parameter updating.
result Improves speed and accuracy by up to 99% and 56%.
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.
New neural network training method uses bi-fidelity data to reduce errors.
problem Training neural networks with limited high-fidelity data.
method Bi-fidelity -regularization strategies.
result Bi-fidelity -regularization reduces errors by one order of magnitude.
Unified geometric principles unify neural network architectures.
problem High-dimensional learning tasks with underlying low-dimensionality and structure.
method Unified geometric principles applied to neural network architectures.
result Unified mathematical framework for neural network architectures.
The radial Newton problem: nonlinear dynamics of minimal resistance in central fieldsphysics.flu-dyn
The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.
problem Nonlinear dynamics of minimal resistance in radial fields.
method Analysis of two non-equilibrium scenarios: scale-invariant free expansion and incompressible source flow.
result Incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions.
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.
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
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 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.
Paper optimizes ES estimation under an constraint, reducing estimation errors.
problem High instability and infeasibility of ES estimation above a critical ratio .
method Analytical approach using the method of replicas from statistical physics.
result Regularization with constraint renormalizes the aspect ratio .
We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are given for the `product' of two Sasakian-Einstein manifolds to be a smooth Sasaki…
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.
Enforcing Deterministic Constraints on Generative Adversarial Networks for Emulating Physical Systemsphysics.comp-ph
Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical question must be answered before GANs can be considered trusted emulators for physi…
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.
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.
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
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.
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the em…
An interpretation of the Brownian bridge as a physics-informed prior for the Poisson equationstat.ML
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.
We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The network is used to simulate the dynamic behavior of physical quantities (i.e. saturation) subject to a set of g…