2021/01/14 by Sebastian Kaltenbach, Kaltenbach, Sebastian, Phaedon‐Stelios Koutsourelakis +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2101.05834
openalex publication_date 2021/01/14 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28
Given (small amounts of) time-series' data from a high-dimensional,\nfine-grained, multiscale dynamical system, we propose a generative framework\nfor learning an effective, lower-dimensional, coarse-grained dynamical model\nthat is predictive of the fine-grained system's long-term evolution but also of\nits behavior under different initial conditions. We target fine-grained models\nas they arise in physical applications (e.g. molecular dynamics, agent-based\nmodels), the dynamics of which are strongly non-stationary but their transition\nto equilibrium is governed by unknown slow processes which are largely\ninaccessible by brute-force simulations. Approaches based on domain knowledge\nheavily rely on physical insight in identifying temporally slow features and\nfail to enforce the long-term stability of the learned dynamics. On the other\nhand, purely statistical frameworks lack interpretability and rely on large\namounts of expensive simulation data (long and multiple trajectories) as they\ncannot infuse domain knowledge. The generative framework proposed achieves the\naforementioned desiderata by employing a flexible prior on the complex plane\nfor the latent, slow processes, and an intermediate layer of physics-motivated\nlatent variables that reduces reliance on data and imbues inductive bias. In\ncontrast to existing schemes, it does not require the a priori definition of\nprojection operators from the fine-grained description and addresses\nsimultaneously the tasks of dimensionality reduction and model estimation. We\ndemonstrate its efficacy and accuracy in multiscale physical systems of\nparticle dynamics where probabilistic, long-term predictions of phenomena not\ncontained in the training data are produced.\n