Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models

• URL: http://arxiv.org/abs/2008.01915v2
• Date: Sun, 21 Mar 2021 02:06:01 GMT
• Title: Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models
• Authors: Liu Yang, Constantinos Daskalakis, George Em Karniadakis
• Abstract summary: We propose a new method for inferring the governing ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants. Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space.
• Score: 27.623119767592385
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks (GANs). We refer to this method as generative "ensemble-regression" (GER), in analogy to the classic "point-regression", where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Levy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

Related papers

• Electrostatics-based particle sampling and approximate inference [0.0]
  A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced. A discrete-time, discrete-space algorithmic design is provided for usage in more general inference problems.
  arXiv  Detail & Related papers  (2024-06-28T16:53:06Z)
• Causal Modeling with Stationary Diffusions [89.94899196106223]
  We learn differential equations whose stationary densities model a system's behavior under interventions. We show that they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2023-10-26T14:01:17Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics [61.44793171735013]
  We introduce a novel unified architecture, termed latent variation models, which combines the latent learning of cutting-edge generative art approaches with an end-to-end variational framework. Our unified approach achieves a distribution-free distance to the truth of over 20 times less than non-latent state-of-the-art baseline.
  arXiv  Detail & Related papers  (2023-05-17T17:43:10Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain [0.0]
  We provide two explicit applications of the formalism in the context of the so-called tight-binding model relevant in various contexts in solid-state physics. We consider two forms of interactions: reset of quantum dynamics, in which the density operator is at random times reset to its initial form, and projective measurements performed on the system at random times.
  arXiv  Detail & Related papers  (2021-06-27T09:55:13Z)
• Data-driven discovery of interacting particle systems using Gaussian processes [3.0938904602244346]
  We study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems. We propose a learning approach that models the latent interaction kernel functions as Gaussian processes. Numerical results on systems that exhibit different collective behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data.
  arXiv  Detail & Related papers  (2021-06-04T22:00:53Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories [13.3638879601361]
  We consider systems of interacting particles or agents, with dynamics determined by an interaction kernel. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator.
  arXiv  Detail & Related papers  (2020-07-30T01:28:06Z)
• The entanglement membrane in chaotic many-body systems [0.0]
  In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an entanglement membrane'' in spacetime. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries.
  arXiv  Detail & Related papers  (2019-12-27T19:01:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.