The article reviews how gradient flow systems on hypergraphs connect to information geometry and nonequilibrium physics.
problem Understanding the geometry of perturbed gradient flow systems on hypergraphs.
method Formulating modern nonequilibrium principles within the framework of perturbed gradient flow systems on hypergraphs.
result New concepts like moduli spaces and thermodynamical area are introduced to understand speed limits.
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Work maximization guides machine learning models in adaptive systems.
problem How machine learning models can be optimized for thermodynamic efficiency.
method Introducing thermodynamic principle to compare with maximum-likelihood principle.
result Maximum-work models are equivalent to maximum-likelihood models in adaptive systems.
Schrödinger and Onsager's ideas linked in nonequilibrium thermodynamics.
problem Linking Schrödinger's variational problem with Onsager's nonequilibrium statistical mechanics.
method Analyzing the historical context and comparing the two approaches.
result Schrödinger's ideas have not yet been fully integrated into the classical context of Onsager's work.
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …
Predicts coherence from quantum heat engine noise using machine learning.
problem Predicting coherence in quantum heat engines from nonequilibrium fluctuations.
method Developed a machine learning protocol using K-Nearest Neighbor (KNN) model.
result Machine learning successfully predicts coherence from quantum heat engine noise.
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.
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and…
Machine learning predicts critical points for directed percolation models.
problem Determining critical points for directed percolation models.
method Supervised and unsupervised machine learning algorithms (CNN and DBSCAN) were used.
result Machine learning accurately predicts critical points for both models.
Improved machine learning method estimates entropy production robustly.
problem Estimating entropy production from trajectory data.
method Variational representation of α-divergence loss functions. result Optimal α=−0.5 yields best performance. Diffusion models' speed-accuracy relations derived from thermodynamics.
problem Understanding the trade-off between model speed and accuracy.
method Connecting diffusion models to thermodynamics and optimal transport.
result Speed-accuracy relations derived, providing insights into optimal learning protocols.
The study uses response theory to understand RNNs processing input signals.
problem Understanding how RNNs process sequential data.
method Deriving a Volterra series representation for SRNNs output using response theory from nonequilibrium statistical mechanics.
result SRNNs can be viewed as kernel machines operating on a reproducing kernel Hilbert space associated with the response feature.
New gauge fields modify Fokker-Planck dynamics without changing the stationary state.
problem Understanding and modifying nonreversible dynamics in Fokker-Planck models.
method Formulate nonreversible perturbations as gauge fields, mapping to supersymmetric Hamiltonians, and learning finite forces.
result Learned finite forces can recover the optimal Lyapunov-equation solution in nonconvex landscapes.
We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to …
High-quality image synthesis with diffusion models, achieving state-of-the-art FID score.
problem Generating high-quality images from latent variables.
method Training diffusion probabilistic models with a weighted variational bound, inspired by denoising score matching and Langevin dynamics.
result State-of-the-art FID score of 3.17 on CIFAR10 dataset.
Study uses multi-agent reinforcement learning to control self-assembly with high-resolution external control.
problem Designing effective external control protocols for self-assembly with high-resolution control.
method Investigated a multi-agent reinforcement learning approach, comparing fully decentralized and partially decentralized strategies.
result Partially decentralized approach outperforms fully decentralized in controlling self-assembly towards target structures.
It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displa…
Paper variates Navier-Stokes-Fourier system for thermodynamic consistency.
problem Modeling compressible fluid dynamics with thermodynamic constraints.
method Variational discretization with discrete exterior calculus.
result Derives a nonholonomic variational integrator for NSF system.
New algorithm improves latent variable model estimation.
problem Estimating parameters in latent variable models.
method Jarzynski-adjusted Langevin algorithm (JALA) for SMC methods.
result JALA-EM provides maximum marginal likelihood estimate.
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of availa…
TACE unifies scalar and tensorial modeling in Cartesian space for accurate, stable, and efficient atomistic predictions.
problem Complexity and challenges in equivariant atomistic machine learning models.
method Tensor Atomic Cluster Expansion (TACE) in Cartesian space, decomposing local environments into irreducible Cartesian tensors (ICT).
result Universal invariant and equivariant embeddings, enabling explicit control at inference.
Introduces new info-geometric structure for dynamics on graphs and hypergraphs.
problem Modeling dynamics on discrete structures like graphs and hypergraphs.
method Introduces two dually flat structures: one on vertex space and another on edge space.
result Extends gradient flows to include nonequilibrium dynamics.
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.
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.
Higher topos theory applied to physics.
problem No specific problem stated.
method Exposition of higher topos theory.
result No specific key result mentioned.
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution P to another distribution Q enables the solution to many problems in machine learning (e.g. Bayesian inference…
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.
Discussing AI's difficulty and physics' simplicity, suggesting AI benefits from physics principles.
problem AI difficulty compared to physics simplicity.
method Drawing on physical intuition and theoretical physics to improve AI.
result AI and physics principles are strongly coupled through sparsity.
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.
Special issue on understanding physical processes from unusual diffusion patterns.
problem Understanding physical processes from anomalous diffusion data.
method Not explicitly described in the abstract, but likely involves analysis of data from the Anomalous Diffusion Challenge.
result Not explicitly stated, but likely includes analysis of physical processes from anomalous diffusion data.
Unified approach to denoising Markov models for efficient sampling.
problem Designing efficient sampling algorithms for complex distributions.
method Mathematical foundation using measure transport and nonequilibrium statistical mechanics.
result Unified variational objective and backward generator construction.
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price fluctuations as a non-Markovian stochastic process using the first-passage stat…
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.
Machine learning improves planetary space physics by incorporating physical knowledge.
problem Improving performance and interpretability of machine learning models for planetary space physics.
method Building on a previous semi-supervised physics-based classification, the team used varying data and physical information to improve machine learning performance and interpretability.
result Incorporating physical knowledge improves machine learning performance and interpretability, essential for deriving scientific meaning.
NNs accurately predict energy eigenvalues and other physical phenomena in 1D quantum mechanics.
problem Understanding how neural networks interpret physics.
method Training NNs to predict energy eigenvalues from potentials and testing their ability to generalize.
result NNs can predict physical phenomena not learned during training, indicating a new way of understanding physics.
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.
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.
DPC uses physics and neural nets to solve SDEs.
problem Solving stochastic differential equations with missing physics.
method Physics-data fusion with conditional maximum mean discrepancy (CMMD) loss.
result DPC achieves highly accurate solutions on benchmark examples.
Machine learning boosts physics research, especially at high energy experiments.
problem Finding new fundamental physics in high energy experiments.
method Review of machine learning methods and applications in high energy physics.
result Modern machine learning techniques have expanded the scope of physics research.
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.
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…
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. 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…
Single model learns physics from diverse data.
problem Lack of universal physics models for diverse applications.
method General Physics Transformer (GPhyT) trained on diverse physics data.
result Single model achieves superior performance across multiple physics domains.
Improves machine learning models by incorporating physical laws into feature maps.
problem Lack of model interpretability in classical machine learning approaches.
method Physics-informed feature maps constructed from physical laws and dimensional analysis.
result Enhanced model interpretability and potential discovery of new physical equations.
Several statistical and machine learning methods are proposed to estimate the type and intensity of physical load and accumulated fatigue . They are based on the statistical analysis of accumulated and moving window data subsets with construction of a kurtosis-skewness diagram. This approach was applied to the data gat…
Unified access package for fundamental physics datasets simplifies machine learning.
problem Lack of unified access to datasets from multiple fundamental physics disciplines.
method Unified Python package with common interface and reference models.
result Graph-based neural networks perform similarly to dedicated methods on various datasets.