This paper studies when particle filtering is efficient for planning in partially observed systems.
problem The efficiency of particle filtering for planning in partially observed linear dynamical systems.
method Coupling of ideal and approximate sequences to bound particle complexity.
result Polynomially many particles suffice for stable systems to approximate optimal planning.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
Framework expands particle filtering to estimate states beyond prior boundaries.
problem Limitations of traditional particle filtering in estimating states outside prior support.
method Diffusion-Enhanced Particle Filtering Framework with adaptive diffusion, entropy-driven regularisation, and kernel-based perturbations.
result Framework significantly improves state estimation accuracy and success rates for out-of-boundary targets.
New method optimizes multiple objectives using particle dynamics and gradient flow.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
A new method de-randomizes MCMC dynamics using the Stein operator.
problem Estimating complex target distributions in Bayesian inference.
method De-randomized kernel-based particle samplers that discretize the fiber-gradient Hamiltonian flow.
result GSVGD de-randomizes complex MCMC dynamics, maintaining high sample quality.
GER learns particle dynamics from unpaired snapshots using physics-informed GANs.
problem Learning particle dynamics from unpaired snapshots with physics constraints.
method Physics-informed generative model to fit particle ensemble distributions.
result Inferred dynamics of particle ensembles governed by SODEs up to 100 dimensions.
New method accelerates energetic variational inference using particle dynamics.
problem Efficiently solving variational inference problems with reduced computational cost.
method Particle-based variational inference with implicit scheme, inspired by energy quadratization and operator splitting.
result Significantly reduces computational cost compared to existing methods.
This work finds mixed equilibria in zero-sum games using interacting particle dynamics.
problem Finding mixed equilibrium points in continuous minmax games.
method A method based on entropic regularisation of two-layer zero-sum games with interacting particle dynamics.
result The sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, implying convergence of the empirical measure and the Nikaidô-Isoda error.
MD-GAN learns long-time molecular behavior from short-time data with multi-particle input.
problem Accurately predicting long-time molecular dynamics from short-time data.
method Machine learning method (MD-GAN) that incorporates dynamics of multiple particles of molecules.
result Predicting diffusion with one-third of the training data length using multi-particle input.
Transformers approximate mean-field dynamics of indistinguishable particles.
problem Approximating the dynamics of indistinguishable particles in complex systems.
method Using transformers to model the mean-field dynamics of interacting particle systems.
result Theoretical bounds on the distance between true and transformer-obtained mean-field dynamics.
We report a statistical analysis of the Island ECN (NASDAQ) order book. We determine the static and dynamic properties of this system, and then analyze them from a physicist's viewpoint using an equivalent particle system obtained by treating orders as massive particles and price as position. We identify the fundamenta…
New methods combine MALA and mGRAD for scalable Bayesian inference in high-dimensional state-space models.
problem Bayesian inference in high-dimensional state-space models with limited scalability.
method Combines gradient-based MALA and prior-informed mGRAD for scalable inference.
result Extends classical MCMC methods to handle multiple time steps and particles.
RNN operators solve Newton's equations with large timesteps for molecular dynamics.
problem Solving Newton's equations of motion with large timesteps for molecular dynamics simulations.
method Recurrent Neural Networks (RNN) operators to solve Newton's equations using past trajectory data.
result Significant speedup in molecular dynamics simulations with timesteps up to 4000 times larger.
New methods improve sampling from complex dynamical models.
problem Sampling from high-dimensional, non-linear latent dynamical models is computationally challenging.
method Introduce auxiliary MCMC and Particle Gibbs samplers with improved performance and parallelisation.
result Enhanced samplers maintain performance in high-dimensional latent spaces and support parallelisation.
A new particle filter uses diffusion models to improve state estimation from noisy data.
problem Sequentially estimating the state of a dynamical system from noisy and incomplete observations.
method Uses a diffusion model to simulate and predict system dynamics, incorporating noisy observations to refine predicted states.
result An unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
Gaussian-SVGD dynamics converge to Gaussian distributions under certain conditions.
problem Understanding the theoretical properties of SVGD, especially for Gaussian targets.
method Detailed theoretical study of Gaussian-SVGD dynamics, considering both mean-field PDE and discrete particle systems.
result Gaussian-SVGD dynamics converge linearly to the Gaussian distribution closest to the target in KL divergence.
This work connects point particles to spin chains using geometric methods.
problem Understanding dynamics of free point particles on Riemannian manifolds.
method Kirillov orbit method, geometric quantization, Lagrangian submanifolds.
result Establishes a spectral equivalence between Laplace-Beltrami operator and a spin Hamiltonian.
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining stochastic approximation EM and particle Gibbs with ancestor sampling (PGAS), PS…
Model tracks structural changes in Brownian particle configurations on a sphere.
problem Tracking structural changes in Brownian particle configurations on a sphere.
method Introduces Frustrated Distance Matrix (FDM) model for dynamic distance matrices on S^2.
result Preserves static BBS template with dynamics as redistributed spectral mass.
EnKO combines VI and EnKF for efficient latent dynamics inference.
problem Particle degeneracy and biased gradient estimators in SMC-based methods.
method EnKO: hybrid of VI and EnKF.
result EnKO outperforms SMC-based methods in predictive ability and particle efficiency.
Particles representing tokens cluster in Transformers, influenced by initial tokens and matrix spectrum.
problem Understanding the geometry of learned representations in Transformers.
method Viewing Transformers as particle systems, applying dynamical systems and partial differential equations.
result Particles cluster towards limiting objects, confirming context-awareness and the emergence of leaders.
Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.
problem Approximating dynamics of polynomial-width neural networks with infinite-width networks.
method Bounding approximation gap through a differential equation governed by mean-field dynamics, considering local Hessian.
result Polynomially many neurons are sufficient to closely approximate mean-field dynamics.
Reflective Hamiltonian Monte Carlo struggles with high-dimensional sampling.
problem Slow mixing in reflective Hamiltonian Monte Carlo with inexact reflections.
method Quantifying instantaneous non-uniformity with Sinkhorn divergence; analyzing particle motion in spheres and cubes; constructing low-dimensional toy models.
result Particles spontaneously unmix, leading to resonances in particle density.
Novel approach to Bayesian experimental design for non-exchangeable data.
problem Optimal experimental design for non-exchangeable data.
method Inside-Out SMC2 algorithm embedded in particle Markov chain Monte Carlo framework. result Efficacy demonstrated on a set of dynamical systems.
Study particle dynamics in non-differentiable fractal spaces.
problem Understanding motion in non-smooth, probabilistic geometries.
method Use fiber bundle theory to characterize multivalued geodesic trajectories.
result Developed a hybrid theory combining surface and stochastic process theories.
In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…
We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number …
The ability to track a moving vehicle is of crucial importance in numerous applications. The task has often been approached by the importance sampling technique of particle filters due to its ability to model non-linear and non-Gaussian dynamics, of which a vehicle travelling on a road network is a good example. Partic…
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian…
New methods learn sampling distributions for particle filters without supervision.
problem Designing accurate sampling distributions for nonlinear dynamical systems.
method Proposed four unsupervised learning methods for multivariate Gaussian and nonparametric distributions.
result Learned sampling distributions outperform designed ones in accuracy.
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic dynamics of each individual in a flock, and use a fractional PDE to model the evo…
Two SVGD variants achieve fast convergence with provable guarantees.
problem Understanding and improving SVGD's performance with finite particles.
method Introducing virtual particles and novel stochastic approximations.
result Provable fast convergence rates for finite-particle SVGD variants.
Physics-guided reinforcement learning optimizes swimming in turbulent flows.
problem Optimizing swimming efforts to maintain proximity in turbulent environments.
method Physics-informed actor-physicist reinforcement learning algorithm.
result Physics-informed reinforcement learning outperforms standard methods in turbulent flow control.
Unified ML approach for SDEs in bounded domains.
problem Challenges in simulating SDEs with particle exit phenomena.
method Hybrid approach combining diffusion model and exit prediction network.
result Accurate modeling of interior dynamics and boundary interactions.
LoRA fine-tuning causes forgetting, studied via particle system dynamics.
problem Catastrophic forgetting in LoRA fine-tuning.
method Mean-field self-attention model, partial differential equations, dynamical systems.
result Characterization of phase transitions in forgetting behavior.
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
A method for inferring motility models and heterogeneity from particle trajectories.
problem Understanding motility patterns from discrete trajectory data of biological agents.
method Maximum likelihood approach for second-order Langevin models with population heterogeneity.
result The proposed method outperforms alternative approaches for short trajectories.
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
Improved PoC for MFLD reduces approximation error and provides model ensemble guarantees.
problem Quantifying optimization complexity in mean-field Langevin dynamics.
method Refined defective log-Sobolev inequality for neural network training.
result Improved PoC result with reduced approximation error and theoretical model ensemble guarantees.
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
New method learns latent energy models using particle algorithms.
problem Learning latent variable models with energy priors.
method Continuous-time SDEs for MMLE, particle-based discretization.
result Practical algorithm converges to solve MMLE problem.
In this paper we continue our analysis of a formulation of electrodynamics fully covariant under the full Poincaré group. Transformations under the four different components of the group force on us the introduction of particles, either in the identification by Feynman or in the identification of Dirac.
The paper proposes a GP-based method for discovering second-order particle dynamics models.
problem Discovering a general second-order particle-based model for agent interactions.
method Gaussian Process-based approach integrating two independent GP priors on latent interaction kernels.
result The method learns effective nonlinear dynamics representations from small data sets.
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …