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

Source: [Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantification](<https://www.sota2.com/research/paper/68fa59c31e209131ce9ba1c0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-01T12:30:38.435Z

Authors: Ruoxi Jiang, Rebecca Willett

Published: 2022-11-03T01:59:20.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Continuous Ranked Probability Score (CRPS) Estimation on Lorenz-96 200 samples (test)](<https://www.sota2.com/research/sota/continuous-ranked-probability-score-crps-estimation-on-lorenz-96-200-samples-test.md>): Continuous Ranked Probability Score (CRPS) Estimation; Lorenz-96 200 samples (test); CRPS Component F: 0.36.

- [Parameter Estimation on Multiscale Lorenz-96 (test)](<https://www.sota2.com/research/sota/parameter-estimation-on-multiscale-lorenz-96-test.md>): Parameter Estimation; Multiscale Lorenz-96 (test); Mean AP Error (F): 6.3.

- [Parameter Estimation on Kuramoto-Sivashinsky Equation (KSE) (test)](<https://www.sota2.com/research/sota/parameter-estimation-on-kuramoto-sivashinsky-equation-kse-test.md>): Parameter Estimation; Kuramoto-Sivashinsky Equation (KSE) (test); MAPE (lambda\_2): 0.0324.

- [Uncertainty Quantification on Kuramoto-Sivashinsky (KS) equation 100 instances (test)](<https://www.sota2.com/research/sota/uncertainty-quantification-on-kuramoto-sivashinsky-ks-equation-100-instances-test.md>): Uncertainty Quantification; Kuramoto-Sivashinsky (KS) equation 100 instances (test); CRPS (λ\_s): 0.121.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2211.01554>)

[PDF](<https://arxiv.org/pdf/2211.01554.pdf>)

[Implementation](<https://github.com/roxie62/Embed-and-Emulate>)