Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
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.
Paper studies systemic robustness in financial networks using particle systems.
problem Budget control and default risk in regional financial networks.
method Mean-field particle system approach, McKean-Vlasov equations, asymptotic analysis.
result Systemic robustness measured by the proportion of surviving entities in large particle systems.
Coercivity condition ensures learning of interacting particle systems.
problem Ensuring identifiability of interaction functions in learning systems of interacting particles.
method Equivalence of coercivity condition to strictly positive definiteness of an integral kernel.
result For ergodic systems, the integral kernel is strictly positive definite, satisfying the coercivity condition.
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
We investigate unification of two systems of identical elements having different dimensions which may be of interest for both physics and economics. Characteristic parameters as well as explicit formulae for the temperature (in economics - capital turnover) and dimension of the united system are obtained as functions o…
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …
Bayesian inference for neural networks improves uncertainty quantification.
problem Improving predictive uncertainty in neural networks.
method Ensemble Kalman filter extensions and interacting particle systems.
result Effective methods for quantifying predictive uncertainty in neural networks.
Particle filtering is a powerful approach to sequential state estimation and finds application in many domains, including robot localization, object tracking, etc. To apply particle filtering in practice, a critical challenge is to construct probabilistic system models, especially for systems with complex dynamics or r…
This work develops a particle system to approximate Fisher-Rao gradient flows in mean-field optimization.
problem Optimizing probability measures in neural network contexts.
method Constructing an interacting particle system approximating Fisher-Rao gradient flows.
result Propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization.
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.
Magnetic particle imaging (MPI) data is commonly reconstructed using a system matrix acquired in a time-consuming calibration measurement. The calibration approach has the important advantage over model-based reconstruction that it takes the complex particle physics as well as system imperfections into account. This be…
Develops a new algorithm for estimating model parameters using interacting particle systems.
problem Estimating parameters of latent variable models.
method Interacting Particle Langevin Algorithm (IPLA) based on Langevin diffusion.
result Nonasymptotic optimisation error bounds for the estimator.
In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the relevant information of the nonlinear system is captured by an unknown state vecto…
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
Method identifies IPS governing equations from particle data efficiently.
problem Identify governing equations of interacting particle systems efficiently.
method Combines mean-field theory and WSINDy for large N and M. result Converges with rate O(N−1/2) for N≥100. We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to t…
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…
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.
New method learns particle system potentials from unlabeled data.
problem Learning potentials of interacting particle systems from unlabeled data with trajectory information missing.
method Introduces a self-test loss function based on stochastic evolution equation.
result Method outperforms baseline methods in robust estimation of large, high-dimensional systems.
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.
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this …
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 identifies unique minimizers for interaction kernels in particle systems.
problem Identifying unique interaction kernels in mean-field equations of interacting particles.
method Data-adaptive L2 spaces, RKHS analysis, regularization. result Characterization of identifiability in both finite and infinite particle systems.
New algorithm trains latent diffusion models using interacting particles.
problem Training latent diffusion models efficiently and accurately.
method Reformulate training as minimizing a free energy functional, then approximate with interacting particles.
result The new algorithm outperforms previous methods in experiments.
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.
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.
Bayesian inference reconstructs external potentials in DFT for many-particle systems.
problem Reconstructing external potentials in classical density-functional theory (DFT) for many-particle systems.
method Combines Bayesian inference with classical DFT to probabilistically reconstruct external potentials.
result Accurately infers external potentials and density profiles with uncertainty quantification.
A new method estimates time-varying parameters in earth system models using offline and online data assimilation.
problem Estimating time-varying parameters in complex earth system models.
method Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF)
result HOOPE-PF outperforms existing methods, especially with small ensemble sizes.
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…
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
Model financial default cascades on sparse graphs via hitting times.
problem Capturing systemic risk in large, sparsely-connected financial networks.
method Dynamic particle systems with hitting times and convergence theory.
result Characterization of default time distribution in tree-like networks.
Machine learning predicts phase behavior in active matter suspensions.
problem Predicting phase behavior in active matter systems using machine learning.
method Used deep learning techniques, including fully connected networks and graph neural networks, to predict motility-induced phase separation (MIPS) in ABP suspensions.
result Strong agreement between machine learning predictions and MIPS binodal from simulations, suggesting machine learning as an effective method for phase behavior determination.
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It…
New approach reduces particle simulation complexity to linear time and space.
problem Challenges in learning dynamics from particle interactions, especially N-body problems.
method Transforms fully-connected interaction graphs into hierarchical ones, reducing complexity.
result Linear time and space complexity for large-scale simulations, retaining high accuracy.
Electrostatics method samples complex distributions deterministically.
problem Sampling and inference of complex, high-dimensional distributions.
method Electrostatics-based particle system with Newton mechanics principles.
result Method achieves comparable performance to other methods in benchmark tasks.
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the existence of periodic motions for such particles under a condition of positivity of …
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.
Algorithm learns interaction kernels for particle systems from data.
problem Understanding and modeling interactions in systems of interacting particles.
method Nonparametric algorithm using least squares with regularization, probabilistic error functional, and reproducing kernel Hilbert space convergence.
result The algorithm converges optimally and accurately learns interaction kernels.
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 study an interacting particle system in Rd motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization. We prove that in the large particle limit the empirical measure of the particle s…
DMPS uses diffusion maps and LAWGD for efficient generative modeling.
problem Efficiently modeling complex data distributions.
method Diffusion maps for manifold learning and LAWGD for sampling.
result DMPS outperforms other methods on moderate-dimensional data.
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.
Gaussian process framework learns interaction kernels in multi-species particle systems.
problem Learning interaction kernels in multi-species interacting particle systems from trajectory data.
method Nonparametric Bayesian approach with Gaussian processes.
result Established rigorous statistical guarantees for recoverability and optimality of interaction kernels.
New AD methods improve likelihood estimation for partially observed systems.
problem Estimating likelihood functions for partially observed nonlinear systems.
method Embedding AD particle filter methods in a theoretical framework, developing new algorithms for likelihood maximization.
result Mean squared error significantly lower than existing algorithms.
The homogeneous canonical formalism of Rund is applied to the second-order Lagrangian model of the self-interacting particle of Bopp. The quasi-classical free spinning particle of Mathisson appears then as a constrained subsystem of the previous system. Differential-geometric mechanisms offered in this work are formula…