New neural network enforces mass conservation for better ice flow predictions.
problem Reliably project future sea level rise by improving ice sheet model inputs.
method Proposes divergence-free neural networks (dfNNs) enforcing local mass conservation.
result dfNNs yield more reliable ice flux estimates compared to other models.
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By con…
INO learns physical models with momentum conservation laws.
problem Learning physical models without preserving fundamental laws.
method Designing an invariant neural operator that automatically satisfies momentum conservation laws.
result The model learns complex material behaviors and achieves state-of-the-art accuracy and efficiency.
Framework infers conservation laws from trained neural networks.
problem Building reduced models of complex systems from physical data.
method Derives conservation laws from symmetries of dynamics in trained DNNs using Noether's theorem.
result Consistent results with previous studies for metastable collective motion systems.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
problem Challenges in applying physics-inspired NNs to real-world systems.
method Examined and relaxed inductive biases of Hamiltonian NNs, improving performance on non-conservative systems.
result Improved performance on practical, non-conservative systems by relaxing inductive biases.
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which admit potential symmetries. Then by using the partial Lagrangian approach, we fi…
LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.
problem Neural networks struggle to learn physical symmetries like conservation laws.
method Lagrangian Neural Networks (LNNs) parameterize arbitrary Lagrangians using neural networks.
result LNNs conserve energy and relativity in complex systems.
Simplified kernel ridge regression with a conservation law.
problem Understanding the test risk and generalization of kernel ridge regression.
method Identification of a conservation law that limits KRR's learning ability, leading to simplified expressions for test risk.
result Transparency in test risk expressions through the conserved quantity in the kernel eigenbasis.
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.
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
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.
Novel method combines physics priors for energy-conserving dynamics.
problem Learning long-term dynamics of complex physical systems from noisy data.
method Variational Integrator Graph Networks integrating energy constraint, high-order symplectic integrators, and graph neural networks.
result Improves predictive performance across single and many-body problems.
Physics-informed semantic inpainting improves geostatistical modeling by incorporating indirect measurements.
problem Inferring heterogeneous geological fields from limited measurements and prior spatial statistics.
method Proposes a physics-informed semantic inpainting framework using WGAN-GP to incorporate both direct and indirect measurements.
result The method satisfies physical conservation laws and enhances inpainting performance compared to using only direct measurements.
In this short Note we would like to bring into the attention of people working in General Relativity a Schwarzschild like metric found by Professor Cleopatra Mociuţchi in sixties. It was obtained by the A. Sommerfeld reasoning from his treatise "Elektrodynamik" but using instead of the energy conserving law from the cl…
LDDNN learns physical dynamics from data without exact solutions.
problem Learning physical dynamics from data without exact solutions.
method LDDNN topology that learns Lagrangian density from data.
result LDDNN can learn physical dynamics from data.
GeoHNN models physics laws for stable, accurate predictions.
problem Violations of physical principles in machine learning models.
method Explicitly encodes geometric priors in inertia and phase space.
result Significantly outperforms existing models in long-term stability and accuracy.
The paper improves ODE solvers by integrating diverse information types.
problem Improving accuracy and physical meaningfulness of ODE solutions.
method Leveraging probabilistic solvers to include second-order information and physical conservation laws.
result Solutions become more accurate and physically meaningful with additional information.
This work connects symmetries and conserved quantities in machine learning.
problem Improving machine learning models by learning conserved quantities.
method Using Noether's theorem, learn symmetries and conserved quantities directly from data.
result Correctly identifies conserved quantities and improves model performance.
Enhances HNNs for conservative systems with noisy data.
problem Modeling conservative systems with neural networks.
method Proposes a deep hidden physics model for continuous-time trajectory estimation.
result Integration scheme works well for HNNs, especially with low sampling rates.
MC-LSTM extends LSTM to conserve mass in neural networks.
problem Conservation laws in real-world systems.
method Extending LSTM's inductive bias to conserve mass.
result MC-LSTM sets new state-of-the-art for predicting peak flows.
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.
Phase2vec learns embeddings of dynamical systems without supervision.
problem Predicting the classes of 2D dynamical systems from data.
method Physics-informed convolutional network that extracts geometric features and minimizes reconstruction loss.
result Learned embeddings respect the semantics of physical systems and outperform blackbox classifiers.
Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.
problem Learning physics of complex systems from incomplete experimental data.
method Integrates port-metriplectic formalism with neural networks to enforce thermodynamics principles.
result Neural networks can learn physics of complex systems by parts, reducing learning burden.
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…
Paper introduces a method to generate physically feasible dynamics with physical priors.
problem Challenges in generating physically feasible dynamics under physical priors.
method Seamlessly incorporates physical priors into diffusion-based generative models.
result Efficient generation of physically realistic dynamics across various physical phenomena.
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an n-dimensional manifold with a metric of Lorentzian signature. In general, the completely …
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of …
Develops ECD framework for optimizing machine learning problems.
problem Optimizing machine learning models, especially non-convex ones.
method Energy Conserving Descent (ECD) framework, chaotic dynamical systems.
result ECDSep outperforms existing methods on various machine learning tasks.
This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of surface Hamiltonians. The ground state for the gravitational energy is taken to…
Framework learns physics-informed continuum models from molecular data.
problem Discovering accurate and robust data-driven continuum models from molecular simulation data.
method Operator regression framework using neural networks in modal space with physical inductive biases.
result Learned operators generalize to unseen system characteristics.
New energy measure for isolated systems in general relativity.
problem Quantifying energy in isolated systems in general relativity.
method Optimal isometric embedding and conformal Killing fields.
result Finite quasi-local energies for asymptotically flat spacetimes.
Automates discovery of interpretable Lagrangians from data.
problem Lack of interpretable Lagrangian discovery methods.
method Data-driven machine learning algorithm to derive interpretable Lagrangians.
result Automated discovery of interpretable Lagrangians and conservation laws.
Develops weak PINNs for efficient manifold solutions of hyperbolic equations.
problem Challenges in approximating weak solutions of nonlinear hyperbolic equations on manifolds.
method Introduces a novel weak PINN (wPINN) formulation on manifolds leveraging well-posedness theory.
result Demonstrates efficient approximation of entropy solutions on manifolds with a complexity independent of ambient space dimension.
Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
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 …
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is achieved starting only from a given quadratic Hamiltonian function of polymomenta H…
This is an invited article for the Discussion and Debate special issue of The European Physical Journal Special Topics on the subject "Can Economics Be a Physical Science?" The first part of the paper traces the personal path of the author from theoretical physics to economics. It briefly summarizes applications of sta…
Parsimonious neural networks discover interpretable physical laws from data.
problem Discovering interpretable physical laws from data using machine learning.
method Combining neural networks with evolutionary optimization to balance accuracy and parsimony.
result Developed models for classical mechanics and materials melting temperature prediction.
This study compares different thermodynamic structure-informed neural networks for solving differential equations.
problem Improving the accuracy and physical consistency of neural network solutions to differential equations.
method Comprehensive evaluation of various thermodynamic formulations in physics-informed neural networks.
result Newtonian-residual-based PINNs fail to reliably recover physical quantities, while structure-preserving formulations enhance accuracy and robustness.
Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first and second case the investigation is reduced to the analysis of the nonidentical …
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…
We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group…
Paper predicts turbulent flows using physics-informed deep learning.
problem Predicting turbulent flows from fluid simulations.
method Hybrid approach combining RANS and LES with trainable spectral filters and U-net.
result Significant reduction in prediction error for 60 frames ahead.
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.
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealt…
Physics-constrained GANs generate samples that meet deterministic constraints.
problem Ensuring GAN-generated samples comply with physical constraints.
method Enforce deterministic constraints via modified loss function.
result Physics-constrained GANs produce samples that accurately meet underlying constraints.
Imagine that measurements are made at times t0 and t1 of the trajectory of a physical system whose governing laws are given approximately by a class A of so-called {\em prior vector fields}. Because the physical laws are not known precisely, it might be that the measurements are not realised by the integ…
Analyzes symmetries in neural networks to predict learning dynamics.
problem Understanding the dynamics of neural network parameters during training.
method Unified theoretical framework based on symmetries and conservation laws.
result Symmetries impose geometric constraints on gradients and Hessians, leading to conservation laws.