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…
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48 results for “physical laws”
Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
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.
INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservationcs.LG
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.
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data is challenging without simultaneously proposing an accompanying discrepancy model…
The paper connects neural networks to physics using probability theory.
problem Creating neural networks that follow physical laws.
method Applying the central limit theorem and Gaussian process theory to neural networks.
result Neural networks can be designed to obey physical laws by choosing appropriate activation functions.
Tensor networks help learn complex physical laws from data.
problem Identifying non-linear dynamical laws from complex physical systems.
method Tensor network parameterizations and rank-adaptive optimization.
result Optimal tensor network models can be learned from data.
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.
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.
Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networksphysics.data-an
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a reduced model of such complex systems on the basis of insights alone. We propose a nov…
Paper applies fluid dynamics to stock market behavior.
problem Understanding stock market dynamics using physical principles.
method Uses Stokes law to model stock market as fluid system.
result Stock market dynamics can be explained by physical properties.
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…
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 …
Micro-Macro Relation of Production - The Double Scaling Law for Statistical Physics of Economy -q-fin.GN
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…
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…
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.
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.
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…
This short note is intended as a "Letter to the Editor" Perspective in order that it serves as a contribution, in view of reaching the physics community caring about rare events and scaling laws and unexpected findings, on a domain of wide interest: sport and money. It is apparent from the data reported and discussed b…
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 …
Analyzes intrinsic time in financial markets, linking it to physical time.
problem Understanding the intrinsic nature of time in financial data.
method Presented an analytic relationship linking intrinsic and physical time, using empirical scaling laws.
result A novel empirical scaling law relating intrinsic time variability to overshoots.
New neural scaling law found for simple quadratic function.
problem Neural scaling laws and their predictions for model performance.
method Analysis of neural networks, lottery ticket ensembling, statistical interpretation.
result Found a new scaling law () for a simple quadratic function, contradicting previous theories.
De la structure des espaces fibrés aux équations fondamentales de la physique. Une introductionphysics.class-ph
This text explains how fiber bundle structure is fundamental for classical physics.
problem None explicitly stated, but implied as understanding fiber bundles is crucial for physics.
method Explains the fiber bundle structure and its universality for physics laws.
result Fiber bundle structure is fundamental for classical physics laws.
Unified bounds for neural networks incorporating physical laws.
problem Limitations in existing generalization analyses for PINNs and VPINNs.
method Unified framework using Taylor expansion and Koopman-based analysis.
result High-rank networks can generalize well even with differential operators.
Bayesian framework discovers interpretable Lagrangian from data.
problem Discovering physical laws from limited data.
method Sparse Bayesian approach for learning interpretable Lagrangian.
result Automates Hamiltonian discovery from Lagrangian and provides ODE/PDE descriptions.
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 two part treatise, we present our developments in the context of solving two main classes …
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of these methods on complex engineered systems. Dynamics of these systems play a cru…
Physics-informed IFT models physical systems with uncertainty, independent of numerical schemes.
problem Modeling physical systems with unknown elements like missing parameters and noisy data.
method Physics-informed Information Field Theory (PIFT) that combines measurements with physical laws, independent of numerical schemes.
result PIFT can capture multiple modes and solve ill-posed problems, robust to model-form uncertainty.
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.
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness…
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.
New model uses symmetries and scaling laws to predict consumer advertising response.
problem Understanding consumer response to advertising efforts.
method Introduces a physics-based mathematical model to describe consumer response dynamics.
result The model better captures nonlinearities in advertising effects and provides new parameters for audience engagement.
Bayesian model learns physics laws from data with uncertainty quantification.
problem Lack of uncertainty in discovering governing physical laws from data.
method Bayesian approach with leaf and root modules, Gaussian process for operators, automatic differentiation.
result Quantifies reliability of learned physics laws and propagates uncertainty.
New method uses scalars to approximate physics functions.
problem Designing neural networks that respect physical symmetries.
method Parameterizing polynomial functions equivariant to various symmetries using scalars.
result Universal approximation of polynomial functions under various symmetries using scalars.
Benchmark tests LLMs on discovering physics laws in unconventional worlds.
problem Difficulties in distinguishing genuine reasoning from recall in LLMs across physics evaluations.
method Interactive benchmark with 22 worlds governed by various unconventional physics laws, requiring agents to design experiments and revise hypotheses.
result Strongest agents fail on worlds requiring latent structure discovery, highlighting limitations in long-term reasoning.
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.
Gradually Truncated Log-normal distribution - Size distribution of firmscond-mat.stat-mech
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
On a Schwarzschild like metricphysics.hist-ph
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…
Deep learning's success is puzzling from a statistical perspective.
problem Deep learning's success is puzzling from a statistical perspective.
method Physics-informed investigation of deep learning features and surprises.
result Neural scaling laws and their interplay with inductive biases.
We introduce a new strategy designed to help physicists discover hidden laws governing dynamical systems. We propose to use machine learning automatic differentiation libraries to develop hybrid numerical models that combine components based on prior physical knowledge with components based on neural networks. In these…
Physics of Personal Incomecond-mat.stat-mech
We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition …
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.
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…
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should seek alternatives. Fortunately, many of the laws of behaviour of the physical wor…
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…
Researchers study how skills are learned in neural networks using physics principles.
problem Understanding how skills are sequentially learned in neural networks.
method Abstract and simplify the problem using physics principles, proposing three models: Geometry, Resource, and Domino.
result Models reveal insights into neural scaling laws, learning dynamics, and the benefits of modularity.
Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEsstat.ML
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 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.