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.
We explain the meaning of local symmetries in physics.
problem Understanding the meaning of local symmetries in physics.
method We argue that general covariance and gauge principles are principles of epistemic access to physical laws, leading to ontological insights.
result Relationality is a core notion in gauge field theory, encoded by local symmetries.
Kichenassamy's work spans theoretical physics, from relativity to applications.
problem Clarifying the postulational basis of relativity theories.
method Introducing the C-equivalence principle to replace the strong equivalence principle.
result New insights into measurements in both special and general relativity.
The paper extends physics-based information maximization to complex bandit problems.
problem Designing efficient decision-making policies for complex bandit problems.
method Information and free-energy maximization principles adapted to three distinct bandit types.
result Information maximization leads to strong performance in complex bandit problems.
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.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
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.
New bandit algorithm maximizes information gain.
problem Optimizing decision-making in uncertain environments.
method Approximates information maximization using entropy and free energy principles.
result Asymptotic optimality proven for two-armed bandit problem.
Model uses statistical physics principles to predict financial market volatility and returns.
problem Predicting price volatility and expected returns in financial markets.
method Inspired by statistical physics, the study introduces a physical model using Level 3 order book data to measure kinetic energy and momentum.
result The model outperforms traditional and machine learning approaches in forecasting volatility and expected returns.
We consider the concept of equilibrium in economic systems from statistical mechanics viewpoint. A new method is suggested for computing the premium on this basis. The Bühlmann economic premium principle is derived as a special case of our method.
AIF improves physical AI agents' performance in dynamic environments.
problem Physical AI agents are less capable than biological agents in open-ended real-world environments.
method Developed from probability theory, Bayesian machine learning, variational inference, and Active Inference (AIF), grounded in the Free Energy Principle.
result AIF minimizes variational free energy and is well-suited to physical constraints.
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.
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.
Unified taxonomy for ML uncertainty in physics, validated.
problem Uncertainty quantification in machine learning for physics.
method Unified taxonomy, principled validation tools.
result Illustrated validation tools with examples.
Most of the econometric and econophysics models have been borrowed from the statistical physics, and as a cosequence, a new interdisciplinary science called econophysics has emerged. In this paper we planned to extend the analogy between different economic processes or phenomena and processes and phenomena from differe…
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.
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.
This paper presents a continuous variable generalization of the Aoki-Yoshikawa sectoral productivity model. Information theoretical methods from the Frieden-Soffer extreme physical information statistical estimation methodology were used to construct exact solutions. Both approaches coincide in first order approximatio…
Turbo-Sim generates models from physics principles, improving interpretability and flexibility.
problem Transforming particle properties from theory to observation in collider physics.
method Maximizes mutual information between input and output, setting loss term weights.
result Mathematically interpretable and flexible generative models.
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
problem Understanding the principles behind emergent intelligent behaviors in disordered systems.
method Statistical physics approach to charting learning mechanisms and dynamics.
result Uncovering relationships between learning mechanisms and physical dynamics.
Paper reconciles two methods of describing Riemannian spaces.
problem Riemann's length principle and Klein's equality principle in geometry.
method Group-theoretic approach to unify length and equality principles.
result Unified group of diffeomorphisms and gauge rotations for Riemannian spaces.
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.
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.
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…
Blockchain aims to improve trust in AI systems, but lacks systematic studies.
problem Lack of systematic studies on blockchain design principles for AI trust.
method Hybrid qualitative and quantitative studies.
result Vast opportunities for future research and practice in blockchain design.
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic measurings is carried out. Procedures for heterogeneous economic time determinati…
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.
High-precision machine learning reduces particle physics simulations by orders of magnitude.
problem Reducing computational burden in particle physics simulations.
method Developed optimal training strategies and tuned machine learning regressors, including Deep Neural Networks with skip connections and boosted decision trees.
result Significantly reduced computational time by factors of 10^3 to 10^6 over first-principles simulations.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
problem Characterize maximal hypersurfaces in open spacetimes.
method Use a generalized maximum principle to analyze hypersurfaces in spatially open Generalized Robertson-Walker spacetimes.
result Provide new uniqueness and non-existence results for complete maximal hypersurfaces in open Robertson-Walker spacetimes.
In this paper will be applied some principles and methods from econophysics in the case of the direct foreign investitions (D.F.I.), particularised for the Greenfield type, and mixed firms of trade and industrial production (Joint Ventures). To this aim will be used some similarities and parallelisms between the mentio…
We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such that the physical payoff distribution coincides with the (corrected) physical asset…
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…
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…
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.
Extract symbolic models from deep learning with inductive biases.
problem Interpreting and discovering physical principles from deep neural networks.
method Introduce strong inductive biases in GNNs, encourage sparse latent representations, apply symbolic regression.
result Extracted symbolic equations from neural networks, including known force laws and new analytic formulas.
Variationality of conformal geodesics fails in higher dimensions.
problem The variationality of conformal geodesics in higher dimensions.
method Analysis of conformal geodesics in three and higher dimensions.
result Variationality fails in both parametrized and un-parametrized conformal geodesics in higher dimensions.
We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces…
General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will p…
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
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.
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.
One endeavour of modern physical chemistry is to use bottom-up approaches to design materials and drugs with desired properties. Here we introduce an atomistic structure learning algorithm (ASLA) that utilizes a convolutional neural network to build 2D compounds and layered structures atom by atom. The algorithm takes …
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…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due t…
In this paper we state the fundamental principles of the gauge approach to financial economics and demonstrate the ways of its application. In particular, modelling of realistic price processes is considered for an example of S&P500 market index. Derivative pricing and portfolio theory are also briefly discussed.
Enhances neural operators with physics knowledge for more accurate simulations.
problem Improving accuracy and generalization of neural operators for physical systems.
method Jointly learns from original PDEs and simplified forms, incorporating fundamental physics.
result Significant improvement in nRMSE across various PDE problems.
Framework augments physical models with deep learning for complex dynamics forecasting.
problem Forecasting complex dynamical phenomena with partial knowledge.
method APHYNITY framework: decomposes dynamics into physical and data-driven components.
result Framework accurately forecasts system evolution and identifies relevant parameters.
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…