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

• URL: http://arxiv.org/abs/2211.01554v1
• Date: Thu, 3 Nov 2022 01:59:20 GMT
• Title: Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantification
• Authors: Ruoxi Jiang, Rebecca Willett
• Abstract summary: This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. Our task is to accurately estimate a range of likely values of the underlying parameters. On a coupled 396-dimensional multiscale Lorenz 96 system, our method significantly outperforms a typical parameter estimation method.
• Score: 11.353411236854582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Parameter Estimation in Quantum Metrology Technique for Time Series Prediction [0.0]
  The paper investigates the techniques of quantum computation in metrological predictions. It focuses on enhancing prediction potential through variational parameter estimation. The impacts of various parameter distributions and learning rates on predictive accuracy are investigated.
  arXiv  Detail & Related papers  (2024-06-12T05:55:45Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Deep Learning of Dynamical System Parameters from Return Maps as Images [0.0]
  We present a novel approach to system identification using deep learning techniques. We use a supervised learning approach for estimating the parameters of discrete and continuous-time dynamical systems.
  arXiv  Detail & Related papers  (2023-06-20T03:23:32Z)
• Towards black-box parameter estimation [0.0]
  We develop new black-box procedures to estimate parameters of statistical models based on weak parameter structure assumptions. For well-structured likelihoods with frequent occurrences, this is achieved by pre-training a deep neural network on an extensive simulated database.
  arXiv  Detail & Related papers  (2023-03-27T09:39:38Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulation [34.30381620584878]
  To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system. We address the latter problem of estimating parameters through a Bayesian inference approach. We leverage GPU code generation and differentiable simulation to evaluate the likelihood and its gradient for many particles in parallel.
  arXiv  Detail & Related papers  (2021-09-18T03:05:44Z)
• Neural Networks for Parameter Estimation in Intractable Models [0.0]
  We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging. We use data from model simulations as input and train deep neural networks to learn statistical parameters.
  arXiv  Detail & Related papers  (2021-07-29T21:59:48Z)
• Physics-constrained deep neural network method for estimating parameters in a redox flow battery [68.8204255655161]
  We present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium flow battery (VRFB) We show that the PCDNN method can estimate model parameters for a range of operating conditions and improve the 0D model prediction of voltage. We also demonstrate that the PCDNN approach has an improved generalization ability for estimating parameter values for operating conditions not used in the training.
  arXiv  Detail & Related papers  (2021-06-21T23:42:58Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• A User's Guide to Calibrating Robotics Simulators [54.85241102329546]
  This paper proposes a set of benchmarks and a framework for the study of various algorithms aimed to transfer models and policies learnt in simulation to the real world. We conduct experiments on a wide range of well known simulated environments to characterize and offer insights into the performance of different algorithms. Our analysis can be useful for practitioners working in this area and can help make informed choices about the behavior and main properties of sim-to-real algorithms.
  arXiv  Detail & Related papers  (2020-11-17T22:24:26Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)

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.