Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantification

TL;DR

This paper introduces a contrastive learning-based framework for learning emulators that estimate parameters of high-dimensional dynamical systems with uncertainty quantification, significantly reducing computational costs.

Contribution

It proposes a novel method that jointly learns feature embeddings and emulators to replace costly simulations for parameter estimation in complex dynamical systems.

Findings

Outperforms traditional parameter estimation methods on Lorenz 96 system

Achieves accurate parameter estimates with only 1.19% of baseline computation time

Demonstrates the effectiveness of contrastive learning in emulator design

Abstract

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a corresponding multichannel time series. Our task is to accurately estimate a range of likely values of the underlying parameters. Standard iterative approaches necessitate running the simulator many times, which is computationally prohibitive. This paper describes a novel framework for learning feature embeddings of observed dynamics jointly with an emulator that can replace high-cost simulators for parameter estimation. Leveraging a contrastive learning approach, our method exploits intrinsic data properties within and across parameter and trajectory domains. On a coupled 396-dimensional multiscale Lorenz 96 system, our method significantly outperforms a typical parameter estimation method based on predefined metrics and a classical numerical simulator, and with only 1.19% of the baseline's computation time. Ablation studies highlight the potential of explicitly designing learned emulators for parameter estimation by leveraging contrastive learning.