VAE models simulate chaotic particle trajectories in flames.
problem Simulating chaotic particle trajectories in combustion systems.
method Variational autoencoder trained on 3D reconstructed particle trajectories.
result Generated trajectories match experimental data accurately.
We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
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.
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.
Hybrid approach combines transformer and Bayesian filtering for robust multiple particle tracking.
problem Challenges in tracking multiple particles in noisy scenes due to combinatorial explosion of hypotheses.
method Attention-Bayesian hybrid framework using transformer for association and Bayesian filtering for pruning hypotheses.
result Improved tracking accuracy and robustness against spurious detections.
GAN model simulates 3D particle trajectories in flame zones.
problem Simulating 3D Lagrangian particle trajectories in flame zones.
method Generative adversarial network (GAN) model with stochastic and convoluted neural networks.
result Best-trained GAN model produced trajectories indistinguishable from ground truth.
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
Graph Neural Networks model 3D granular flow simulations.
problem Accurate modeling of complex 3D granular flow processes.
method Graph Neural Networks approach to simulate 3D granular flow using LIGGGHTS.
result Machine learning trajectories match physical granular flow processes.
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.
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.
Particle Markov chain Monte Carlo techniques rank among current state-of-the-art methods for probabilistic program inference. A drawback of these techniques is that they rely on importance resampling, which results in degenerate particle trajectories and a low effective sample size for variables sampled early in a prog…
We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze t…
Estimates interaction laws from agent trajectories without assuming their form.
problem Inferring interaction laws from observational data in complex systems.
method Non-parametric statistical learning approach from trajectory data.
result Effectiveness demonstrated in various disciplines, including physics, opinion dynamics, and biology.
Study infers interaction kernels from multiple particle trajectories.
problem Inferring interaction kernels from multiple particle trajectories in stochastic systems.
method Nonparametric inference approach based on regularized maximum likelihood estimator.
result Consistent estimator with near-optimal learning rate independent of state space dimension.
Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the particle reflects from the boundary making the angle of incidence equal the angle of reflection. The bi…
Hamilton flows on Kähler manifold for which all trajectories are H-planar curves (complex analog of geodesics) are considered. These flows are called H-planar. The equation which has to obey the Hamiltonian of H-planar Hamilton flow is received and the method of finding general solution of this equation is propos…
Estimates network structure and interaction rules from multiple agent trajectories.
problem Modeling multi-agent systems on networks from data.
method Jointly infers network topology and interaction kernels using non-convex optimization.
result ORALS estimator is consistent and asymptotically normal under coercivity conditions.
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.
The paper learns particle swarming models from data using Gaussian processes.
problem Understanding the link between individual interaction rules and swarming behavior.
method Proposes a learning approach using Gaussian processes to model latent radial interaction functions and scalar parameters in non-collective friction forces.
result Establishes that a coercivity condition is sufficient for recoverability and provides a finite-sample analysis showing optimal convergence rates.
Algorithm generates private continuous-time data for sensitive domains.
problem Private generation of continuous-time data for sensitive domains.
method Mean-field Langevin dynamics and noisy particle gradient descent.
result Strong privacy guarantees for one-time data contributions.
The second order differential equation dtDγ˙(t)=Fγ(t)(γ˙(t))−∇V(γ(t)) on a Lorentzian manifold describes, in particular, the dynamics of particles under the action of a electromagnetic field F and a conservative force −∇V. We provide a first study on the extendability of its solu…
New method learns fractional order of PDEs from flocking particle simulations.
problem Deriving effective nonlocal influence functions from discrete agent-based models.
method Agent-based model, fractional PDEs, Gaussian process regression, Bayesian optimization.
result Learned Euler equations accurately predict flocking behavior.
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.
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzian Geometry. Our aim here is threefold: to give explicit proofs of some technicalities in the background of the specialists, to show that th…
A new variational method for SSMs improves inference efficiency.
problem Hard variational inference for state space models.
method Proposes variational marginal particle filter (VMPF) based on Rao-Blackwellization.
result VMPF provides tighter variational bounds and sometimes benefits from unbiased reparameterization.
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.
Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.
problem Estimating posterior densities in probabilistic models.
method Variational formulation of particle flow, Fisher-Rao gradient flow, Gaussian and Gaussian mixture approximations.
result Gaussian and Gaussian mixture approximations of Fisher-Rao particle flow reduce to Exact Daum and Huang particle flow under linear Gaussian assumptions.
Jointly estimates flow fields and particle properties from Lagrangian data.
problem Estimating flow fields and particle properties from sparse, noisy Lagrangian data.
method Data assimilation framework coupling Eulerian and Lagrangian models.
result Joint estimation of flow fields and particle properties in various flow regimes.
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.
Improved particle Gibbs sampling by marginalizing parameters.
problem Bayesian inference in high-dimensional state-space models is challenging.
method Marginalized particle Gibbs sampling, combining MCMC and sequential Monte Carlo.
result Marginalization improves performance beyond the Gibbs sampler, scaling linearly.
Paper learns interaction laws from multiple trajectories of heterogeneous systems.
problem Estimating unknown interaction laws from multiple trajectories of heterogeneous systems.
method Nonparametric learning of interaction kernels based on pairwise distances, with convergence guarantees in L2 space. result Estimators converge at optimal min-max rate for 1-dimensional nonparametric regression.
Method learns cell interaction rules from individual trajectories.
problem Inferring interaction rules from heterogeneous cellular data.
method WSINDy for second order IPSs, learning individual cell models.
result Efficiently identifies different species and best-fit models for each.
Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.
problem Improving trajectory inference in applications like particle tracking.
method Generalizes Schrödinger Bridge problem to smooth Gaussian processes, solving the problem on phase space.
result The method outperforms existing methods on real datasets.
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.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
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.
Graph neural networks improve charged particle tracking on FPGAs.
problem Charged particle trajectory determination in high interaction density conditions.
method Graph neural networks (GNNs) embedded in tracker data as graphs, classifying edges as track segments.
result GNNs implemented on FPGAs for charged particle tracking, enabling future HL-LHC experiments.
The automatic reconstruction of three-dimensional particle tracks from Active Target Time Projection Chambers data can be a challenging task, especially in the presence of noise. In this article, we propose a non-parametric algorithm that is based on the idea of clustering point triplets instead of the original points.…
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Adaptive vehicle trajectory prediction for safer autonomous driving.
problem Inability of current methods to guarantee physical feasibility and adapt to human driving policies.
method Bayesian recurrent neural network combining policy and physical models, with gradient-based training and parameter adaptation.
result The proposed method ensures physical feasibility and adaptability to human driving policies.
Kernel methods detect coherent structures in dynamical data.
problem Detecting coherent structures in complex dynamical systems.
method Kernel-based dimensionality reduction techniques and eigendecompositions of RKHS operators.
result Coherent sets of particle trajectories can be computed by kernel CCA.
Paper proposes method for optimal control of unknown systems with latent states.
problem Jointly estimating dynamics and latent states in systems with unmeasurable states.
method Combination of particle Markov chain Monte Carlo methods and scenario theory.
result Probabilistic performance guarantees for optimal input trajectories.
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
A new method solves high-dimensional MFGs using particle-based flow matching.
problem Solving high-dimensional Mean-Field Games (MFGs) is computationally challenging.
method Proposes a particle-based deep Flow Matching (FM) method to update particles and train a flow neural network.
result Proves convergence of the scheme to a stationary point sublinearly and linearly under convexity assumptions.
A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides t…