Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects

• URL: http://arxiv.org/abs/2203.05164v2
• Date: Wed, 1 Nov 2023 20:57:21 GMT
• Title: Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects
• Authors: Megan R. Ebers, Katherine M. Steele, J. Nathan Kutz
• Abstract summary: In modern dynamical systems, discrepancies between model and measurement can lead to poor quantification. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch.
• Score: 4.459306403129608
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used. The choice of method depends on one's intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type. In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.

Related papers

• No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs [56.78271181959529]
  This paper proposes a conceptual shift to modeling low-dimensional dynamical systems by departing from the traditional two-step modeling process. Instead of first discovering a closed-form equation and then analyzing it, our approach, direct semantic modeling, predicts the semantic representation of the dynamical system. Our approach not only simplifies the modeling pipeline but also enhances the transparency and flexibility of the resulting models.
  arXiv  Detail & Related papers  (2025-01-30T18:36:48Z)
• Hybrid Adaptive Modeling using Neural Networks Trained with Nonlinear Dynamics Based Features [5.652228574188242]
  This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations.
  arXiv  Detail & Related papers  (2025-01-21T02:38:28Z)
• eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling [9.52474299688276]
  We introduce a low-rank structured variational autoencoder framework for nonlinear state-space graphical models. We show that our approach consistently demonstrates the ability to learn a more predictive generative model.
  arXiv  Detail & Related papers  (2024-03-03T02:19:49Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• Surrogate Modeling for Physical Systems with Preserved Properties and Adjustable Tradeoffs [0.0]
  We present a model-based and a data-driven strategy to generate surrogate models. The latter generates interpretable surrogate models by fitting artificial relations to a presupposed topological structure. Our framework is compatible with various spatial discretization schemes for distributed parameter models.
  arXiv  Detail & Related papers  (2022-02-02T17:07:02Z)
• Closed-form discovery of structural errors in models of chaotic systems by integrating Bayesian sparse regression and data assimilation [0.0]
  We introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states. If observations are noisy, a data assimilation technique such as ensemble Kalman filter (EnKF) is first used to provide a noise-free analysis state of the system. Finally, an equation-discovery technique, such as the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, closed
  arXiv  Detail & Related papers  (2021-10-01T17:19:28Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics [3.214927790437842]
  Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
  arXiv  Detail & Related papers  (2020-05-29T15:10:43Z)

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.