A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This work maps Boltzmann distributions to ARNNs for better physics-based model approximations.
DPC uses physics and neural nets to solve SDEs.
New method learns physical meanings in learned representations for better downstream tasks.
We explain the meaning of local symmetries in physics.
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…
This work learns models for population dynamics using variational methods and higher-order quadrature.
Machine learning knot invariants with physics applications.
We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in Hölder norms determined by the physical metric, by shear-free smoothly conformally compact vacuum initial data.
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
Abstract: Investigates the role of activation functions in neural networks and their physical basis.
Proposes PI-VAE for solving SDEs with limited measurements.
Improves machine learning models by incorporating physical laws into feature maps.
Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically-consistent deep neural network architectures is an open issue. In the spirit of physics-informed NNs, PDE-NetGen package provides new means to automatically translate phys…
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse accurate observation data are available. Specifically, the two types of multifi…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-r…
Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we will prove the existence and uniqueness for solut…
We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime under the necessary and sufficent assumptions that satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter can be used to d…
Bayesian PINN improves estimation of PDE solutions from noisy data.
We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can be applied, some of them have a physical motivation.
Physics-informed GP regression solves eigenvalue problems by identifying non-trivial eigenspaces.
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type expressions. If machine learning is used for physical problems, inferred from domain knowle…
Machine learning improves planetary space physics by incorporating physical knowledge.
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
Develops a dynamic mean field theory for reinforcement learning.
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/ response mapping can be solve…
This paper introduces VI for physics-informed deep learning, enhancing uncertainty quantification.
Enhances neural operators with physics knowledge for more accurate simulations.
Generative method avoids function estimation for data generation.
Modern physics has demonstrated that matter behaves very differently as it approaches the speed of light. This paper explores the implications of modern physics to the operation and regulation of financial markets. Information cannot move faster than the speed of light. The geographic separation of market centers means…
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variation…
Combines physics-based ML with hierarchical Bayesian techniques for better model performance.
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a mean curvature barrier condition and the timelike convergence condition. Further…
The present paper considers if the new proposed conformal geometrodynamics (CGD) can extend the Nature features compared with general theory of relativity (GTR). The answer for this question can be connected with unique phenomenon arising from Riemann space transition used in GTR, to Weyl space used in CGD. We have in …
We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo integration of a univariate Gaussian by 1068 times while doubling the speed of the Monte…
Paper constructs exotic spacetimes with same physical properties.
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…
Ridge regression linked to Poisson resetting in statistical physics.
A characterization of the foliation by spacelike slices of an -dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some natural assumptions, of physical or geometric nature, all the entire solutions of…
Generative model connects physical properties to latent vectors for solar magnetic patches.
A hybrid physics-ML model predicts FO water flux with high accuracy and uncertainty quantification.
An approach is suggested for analyzing time series by means of resummation techniques of theoretical physics. A particular form of such an analysis, based on the algebraic self-similar renormalization, is developed and illustrated by several examples from the stock market time series.
Intelligent agents need a physical understanding of the world to predict the impact of their actions in the future. While learning-based models of the environment dynamics have contributed to significant improvements in sample efficiency compared to model-free reinforcement learning algorithms, they typically fail to g…
Physics-informed deep learning for PDEs solves forward and inverse problems efficiently.
New method solves supercooled Stefan problem, proving minimal solutions are physical.
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
New metric for probability measures connects physics and geometry.
In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…