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.
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.
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.
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
LSS learns molecular trajectories from MD data.
problem Limited integration time steps in MD simulations.
method Three deep learning networks for slow collective variables, dynamics, and configuration reconstruction.
result Generates ultra-long synthetic folding trajectories.
Optimal control strategies modify wealth inequality variance.
problem Minimizing wealth inequality variance in a market economy.
method Kinetic models and model predictive control for wealth dynamics.
result Control modifies Pareto index of wealth distribution.
This paper uses a kinetic approach to model financial agents and their impact on stock prices and wealth distribution.
problem Understanding power-laws in financial data and the causes behind them.
method A kinetic approach inspired by the Levy-Levy-Solomon model, incorporating model predictive control (MPC) for optimization.
result The stock price distribution exhibits power-law behavior for high-frequency traders and lognormal for long-term investors.
Optimizes feature selection for molecular kinetics models.
problem Selecting interpretable features for kinetic models from molecular dynamics simulations.
method Direct optimization of features without constructing a full kinetic model.
result Direct feature optimization leads to more efficient model selection.
The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and…
New method uses machine learning to analyze catalyst reactions.
problem Understanding complex reaction mechanisms in catalytic materials.
method Combining transient kinetics and machine learning.
result Correct estimates of micro-kinetic coefficients and mechanism.
Grey-box model combines GP with motion data to analyze skiing forces.
problem Analyzing forces in cross-country skiing races.
method Combines motion model formulae with Gaussian process regression.
result Grey-box approach reduces predictive uncertainty by 30-40%.
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…
Improved KLMC for sampling under various conditions.
problem Stable simulation of kinetic Langevin dynamics under different parameters.
method Revisited synchronous Wasserstein coupling analysis with stochastic exponential Euler discretization.
result Exponential integrator can simulate kinetic Langevin dynamics in the overdamped regime with proper time acceleration.
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.
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.
Exact solution found for two-body financial dealer model using kinetic theory.
problem Finding an exact solution for the two-body financial dealer model.
method Exact master-Liouville equations derived using kinetic theory and probability currents.
result Exact order-book profile and average transaction interval derived.
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.
KCS improves parametric maps from PET images by reducing noise and variance.
problem Improving the quality of parametric maps from PET images due to noise.
method Kinetic Compressive Sensing (KCS) method based on a hierarchical Bayesian model and novel reconstruction algorithm.
result KCS produces spatially coherent images and parametric maps with lower noise and better contrast.
Markov state models (MSMs) and Master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variationa…
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is bett…
A new probabilistic model for PET image reconstruction.
problem Conventional PET image reconstruction ignores uncertainty in TACs.
method Probabilistic Graphical Modeling (PGM) with gradient-based iterative algorithm.
result Incorporates uncertainty in TACs, improving image reconstruction.
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…
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.
Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.
problem Improper neck postures lead to musculoskeletal disorders requiring therapy and rehabilitation.
method Integrated use of kinematic and kinetic data with machine learning algorithms.
result 100% accuracy in predicting neck postures using the proposed platform.
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.
We briefly review results on nonlinear kinetic equation of Boltzmann type which describe the evolution of wealth in a simple agents market. The mathematical structure of the underlying kinetic equations allows to use well-known techniques of wide use in kinetic theory of rarefied gases to obtain information on the proc…
Study explores how wealth dynamics change with preferential interactions in kinetic exchange models.
problem Investigate how preferential interactions affect wealth dynamics and distributions in kinetic exchange models.
method Conducted Monte Carlo simulations to explore two types of preferential interactions: one with random selection and another with wealth difference constraint.
result Emergence of quasi-oligarchic societies and segregation into economic classes observed in preferential interactions.
Automated method creates compact chemical models from detailed ones, reducing complexity and improving accuracy.
problem Creating accurate low-dimensional chemical kinetic models from detailed ones is time-consuming and requires expert knowledge.
method Machine Learned Optimisation of Chemical Kinetics (MLOCK) algorithm systematically perturbs sub-models to find optimal compact models.
result Compact models (15 species) retain ~87% fidelity to detailed models, outperforming previous methods.
Firm growth process in the developing economies is known to produce divergence in their growth path giving rise to bimodality in the size distribution. Similar bimodality has been observed in wealth distribution as well. Here, we introduce a modified kinetic exchange model which can reproduce such features. In particul…
We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this model with other similar models.
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.
In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a…
Rate GENERIC extends thermodynamics principles to non-equilibrium systems.
problem Understanding non-equilibrium thermodynamics and its relation to equilibrium thermodynamics.
method Developed a geometrical framework for rate GENERIC, extending Onsager's variational principle.
result Rate GENERIC structure provides a new perspective on thermodynamics in non-equilibrium systems.
New non-kinetic actions on four-manifolds discovered.
problem Finding non-kinetic smooth homotopy coherent actions on four-manifolds.
method Restricting a nontrivial action on a K3 surface and constructing extensions. result First example of a non-kinetic smooth homotopy coherent action of order two on a four-manifold.
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.
Kinetic exchange models have been successful in explaining the shape of the income/wealth distribution in the economies. However, such models usually make some ad-hoc assumptions when it comes to determining the savings factor. Here, we examine a few models in and out of the domain of standard neo-classical economics t…
The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we s…
Compact models for methane/air combustion reduce complexity without sacrificing accuracy.
problem Creating accurate, computationally efficient models for methane combustion.
method Data-oriented three-step methodology: 1) Remove non-essential species, 2) Numerically optimize to key species profiles, 3) Machine learning to refine parameters.
result Produced 19 and 15 species compact models that outperform current state-of-the-art models in accuracy and range of conditions.
Unbiased method for Bayesian posterior means using kinetic Langevin dynamics.
problem Estimating Bayesian posterior means efficiently and accurately.
method Combines advanced splitting methods with enhanced gradient approximations in a multilevel Monte Carlo approach.
result The method achieves unbiased estimates with finite variance and central limit theorem properties.
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.
Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.
problem Sampling from log-concave distributions with superlinear gradient growth.
method Proposes two novel discretizations of kinetic Langevin SDEs, showing contractivity and log-Sobolev inequality.
result Establishes non-asymptotic bounds in 2-Wasserstein distance between sampled distributions and target measures.
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of th…
New proof shows nonholonomic motions are geodesics, minimizing distance.
problem Nonholonomic motion equations are not variational.
method Proved geodesic property of nonholonomic trajectories using Riemannian metrics.
result Nonholonomic motions minimize distance in their manifold.
A fast method learns plasma collision kernels from simulations, improving kinetic models.
problem Improving kinetic models for plasma dynamics beyond the weakly coupled regime.
method Data-driven collisional operator, fast spectral separation method.
result Accurately captures plasma dynamics in moderately coupled regime.
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
problem Understanding the dynamics of Vlasov plasma and its kinetic moments.
method Hamiltonian (Lie-Poisson) analysis and matched pair decomposition.
result Observation of mutual interactions between subdynamics in Vlasov plasma.
Unbiased smoothing method improves accuracy in noisy measurements.
problem Approximating latent Markov process expectations with noisy measurements.
method Coupling Particle Independent Metropolis-Hastings (PIMH) chains.
result Unbiased smoothing estimators for parallel computing and confidence intervals.
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.
Kinetic models predict speculators' strategy can affect market prices.
problem Understanding how speculators' behavior affects market prices in a multi-agent exchange system.
method Developed kinetic equations to model interactions between dealers and speculators, using utility functions and mean quantities.
result Speculators' strategy can drive the price of goods towards a zone with marked utility for their group.