Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive of the fine-grained system's long-term evolution but also of its behavior under different initial conditions. We target fine-grained models as they arise in physical applications (e.g. molecular dynamics, agent-based models), the dynamics of which are strongly non-stationary but their transition to equilibrium is governed by unknown slow processes which are largely inaccessible by brute-force simulations. Approaches based on domain knowledge heavily rely on physical insight in identifying temporally slow features and fail to enforce the long-term stability of the learned dynamics. On the other hand, purely statistical frameworks lack interpretability and rely on large amounts of expensive simulation data (long and multiple trajectories) as they cannot infuse domain knowledge. The generative framework proposed achieves the aforementioned desiderata by employing a flexible prior on the complex plane for the latent, slow processes, and an intermediate layer of physics-motivated latent variables that reduces reliance on data and imbues inductive bias. In contrast to existing schemes, it does not require the a priori definition of projection operators from the fine-grained description and addresses simultaneously the tasks of dimensionality reduction and model estimation. We demonstrate its efficacy and accuracy in multiscale physical systems of particle dynamics where probabilistic, long-term predictions of phenomena not contained in the training data are produced.
翻译:鉴于(数量小)时间序列数据来自一个高度、细微和多尺度动态系统,我们提议一个基因框架,用于学习一个有效、低维、粗粗粗的动态模型,该模型可以预测精细系统的长期演进,也可以预测其在不同初始条件下的行为;我们将微细的模型作为目标,因为这些模型在物理应用(例如分子动态、以代理人为基础的模型)中产生的时,其动态非常不固定,但向平衡的过渡则由未知的缓慢过程决定,而这些过程大多是布鲁特力模拟所无法利用的;基于域知识的方法在很大程度上依靠物理洞察,确定时间缓慢的系统特征,不能执行所学动态的长期稳定性;另一方面,纯粹的统计框架缺乏可解释性,并且依赖大量昂贵的模拟数据(如分子动态、以代理人为基础的模型),因为它们无法利用域内的知识;我们提议的精度框架通过在复杂平面上采用灵活前的精确度,而不是由粗略的精确度模拟来决定;基于域知识制定的方法,其方法在很大程度上依靠物理前期预测过程的精确度;此外,其前定的模型定义需要降低现有数据;而先期数据,其前的变变变的数值,其前的系统则需要降低现有物理和前的数值定义,从而降低其前的数值和深层的模型的模型的变变变变。