New method trains deep neural networks for non-interacting kinetic-energy functionals in DFT.
problem Lack of exact relationship between electron density and non-interacting kinetic energy.
method Variational principle to regularize machine-learned density functionals.
result Excellent results on kinetic-energy functionals for various systems.
Smooth isotopy on cube saves energy with extra dimensions.
problem Constructing an isotopy with infinite kinetic energy.
method Explicit construction of isotopy on [0,1]n. result Existence of isotopy with infinite kinetic energy.
Bayesian inference over admissible histories leads to irreversible kinetics.
problem Modeling irreversible processes in systems with uncertain histories.
method A Gibbs-type measure weighted by energy-dissipation action and observation constraints, interpreted as a Bayesian posterior.
result The measure concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution.
Researchers created an accurate kinetic energy functional for materials modeling.
problem Lack of accurate analytic kinetic energy functionals for large-scale ab initio materials modeling.
method Interpretative machine learning of crystal cell-averaged kinetic energy densities guided by a hybrid Gaussian process regression - neural network (GPR-NN) method.
result Constructed an analytic kinetic energy functional that reproduces Kohn-Sham DFT energy-volume curves with sufficient accuracy.
In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a χ2-distance function and …
Study nonrigid dynamics of unitary groups on Lie groups via kinetic energy metrics.
problem Understanding the dynamics of unitary groups on Lie groups using kinetic energy metrics.
method Least action principle applied to geodesics of the kinetic energy metric on G. result Kinetic energy metric on G is not complete and not invariant. This paper optimizes paths for generative models using kinetic energy.
problem Improving generative model performance and sample quality.
method Investigating and optimizing Gaussian probability paths with kinetic energy.
result Kinetic optimal Gaussian paths simplify particle trajectories and improve model performance.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Generalizes Szebehely's inverse problem to three dimensions.
problem Finding a potential V for given curves in 3D space.
method Extends traditional Szebehely's problem by allowing more general kinetic energy functions.
result New potential functions can generate integral curves including given curves.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…
The paper proves a nonholonomic version of Maupertuis-Jacobi principle and shows that nonholonomic trajectories minimize length.
problem Nonholonomic dynamics and their length minimization.
method Contact bundle formulation and geometric equivalence between problems.
result Regular solutions of nonholonomic mechanical problems are reparametrizations of geodesics with minimized Riemannian length.
Noether's framework reveals symmetry-breaking in neural networks.
problem Understanding the role of symmetry breaking in neural networks.
method Developed a theoretical framework using Lagrangian mechanics.
result Identified 'kinetic symmetry breaking' and its effect on learning dynamics.
DiMS sampler explores neural network loss minima via dissipative dynamics.
problem Sampling reparameterization invariant solutions in neural networks.
method Dynamical system based on kinetic energy with dissipative friction.
result DiMS sampler samples exactly from minimum level sets.
Geometric model for flag waving motion.
problem Modeling the motion of a physical flag.
method Isometric immersion of a square into 3D space with boundary conditions.
result The space of flags is an infinite dimensional manifold.
The paper calculates how random changes affect paths on a complex geometric space.
problem Computing the evolution of paths on a manifold of Riemannian metrics.
method Using diffusion processes and stochastic kinetic energy functional.
result Computed the evolution equation for the Lagrangian.
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densitie…
New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5/2-order L2-accuracy in approximating Hamiltonian flows. New methods achieve linear convergence on broader convex functions.
problem Optimization on broader convex functions with singular or unbounded second derivatives.
method Discretizations of conformal Hamiltonian dynamics.
result Linear convergence on convex functions with singular or unbounded second derivatives.
Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly accurate self-consistent densities and molecular forces are found, indicating the…
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
We study the heat flow in the loop space of a closed Riemannian manifold M as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the h…
An original method, assuming potential and kinetic energy for prices and conservation of their sum is developed for forecasting exchanges. Connections with power law are shown. Semiempirical applications on S&P500, DJIA, and NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock Exchange index IS…
This paper explores machine learning landscapes using molecular energy analogy.
problem Understanding the solution space and nature of predictions in machine learning.
method Analogy with molecular potential energy landscapes to explore machine learning landscapes.
result Emergent properties of machine learning landscapes can be related to molecular structure, thermodynamics, and kinetics.
Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantl…
Zero-energy orbits in the Kepler-Heisenberg problem are self-similar and stratify into three families.
problem Determining the motion of a planet around a sun in the Heisenberg group.
method Analysis of the sub-Riemannian Hamiltonian and sub-Laplacian dynamics.
result Zero-energy orbits are self-similar and stratify into future collision, past collision, and quasi-periodic families.
Physics analogies explain machine learning overfitting control.
problem Understanding and controlling overfitting in machine learning.
method Analogies from physics and biology applied to algorithmic stability and GAN models.
result Physics formulas provide insights into reducing overfitting in machine learning.
Optimal transport with path constraints for distributions of different masses.
problem Comparing distributions with different total masses under path constraints.
method Introduces a model for unbalanced optimal transport with path constraints, proving existence of solutions.
result Existence of solutions to path constrained unbalanced optimal transport for various constraints.
MFM improves generative model interpolations by learning approximate geodesics on data manifolds.
problem Straight interpolations fail to capture dynamics on data manifolds.
method Metric Flow Matching (MFM) learns approximate geodesics by minimizing kinetic energy of a data-induced Riemannian metric.
result MFM outperforms Euclidean baselines, achieving SOTA on single-cell trajectory prediction.
SRVs improve MSMs for Trp-cage miniprotein, revealing new folding states.
problem Constructing high-resolution MSMs for complex protein dynamics.
method Employing SRVs as feature set for MSM construction, leveraging slowest modes identified by SRVs.
result SRV-MSMs reveal new folding states and faster convergence.
This paper prioritizes experience replay in robotics using energy-based principles.
problem Randomly replaying experience in HER leads to inefficient learning.
method Developed an energy-based framework to prioritize hindsight experience in robotic manipulation tasks.
result EBP outperforms state-of-the-art approaches in robotic manipulation tasks.
Unified framework for continuous-state discrete flow matching models.
problem Discrete generative modeling with continuous probabilities.
method Introducing α-Flow, a family of CS-DFM models based on information geometry. result Optimal flow matching loss for α-flow minimizes generalized kinetic energy. RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
Paper tackles intermittent learning for energy-constrained machine learning tasks.
problem Energy-constrained machine learning tasks on intermittently powered systems.
method Developed an algorithm and heuristics for efficient learning under energy constraints.
result Improves energy efficiency by up to 100% and reduces learning examples by up to 50%.
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg sub-Laplacian. The resulting dynamical system is known to contain a fundamental inte…
Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …
The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.
problem Extending Vlasov kinetic theory to time-dependent dynamics.
method Introducing geometric kinetic theories within cosymplectic and cocontact manifolds.
result Alternative realizations of cosymplectic and cocontact kinetic theories linked via Poisson/momentum maps.
Proposes new genetic algorithm rule for market competition.
problem Market competition genetic algorithm rules.
method Econophysics kinetic market model as an evolutionary algorithm.
result New replacement rule for genetic algorithms.
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We the…
A physics-based method improves data interpolators and regression tasks.
problem Improving accuracy and efficiency in function learning.
method Inspired by statistical mechanics, introduces corrections to minimize energy.
result Improves performance in interpolation and regression tasks, especially in high-dimensional spaces.
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum i…
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
Study approximates kinetic VFP in bounded domains using weak compactness.
problem Approximating Vlasov-Fokker-Planck in bounded domains with boundary conditions.
method Weak compactness in weighted Hilbert space, construction of test functions.
result Derives diffusion approximation for Vlasov-Fokker-Planck in bounded domains.
This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
CausalKinetiX identifies stable kinetic models from noisy data.
problem Learning stable and predictive kinetic models from noisy data.
method CausalKinetiX framework for identifying structure from discrete time, noisy observations.
result Causal approach improves generalization and prediction in kinetic systems.
An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy changes due to interactions with other molecules. We pursue this analogy and derive a Bolt…
In this article, we briefly review the different aspects and applications of kinetic exchange models in economics and sociology. Our main aim is to show in what manner the kinetic exchange models for closed economic systems were inspired by the kinetic theory of gas molecules. The simple yet powerful framework of kinet…
VAMPnets uses deep learning to model molecular kinetics from simulations.
problem Computing relevant molecular kinetics from simulations requires expert modeling.
method VAMPnets employs variational approach for Markov processes within neural networks.
result VAMPnets produces accurate kinetic models without requiring manual steps.