تقرير
Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling
| العنوان: | Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling |
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| المؤلفون: | Galioto, Nicholas, Sharma, Harsh, Kramer, Boris, Gorodetsky, Alex Arkady |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Physics (Other) Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning, Mathematics - Dynamical Systems, Physics - Data Analysis, Statistics and Probability, Statistics - Computation |
| الوصف: | This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise. The approach is comprised of three main facets. First, we derive a Gaussian filter for a statistically-dependent, vector-valued, additive and multiplicative noise model that is needed to evaluate the likelihood within the Bayesian posterior. Second, we develop a novel algorithm for cost-effective application of Bayesian system identification to high-dimensional systems. Third, we demonstrate how structure-preserving methods can be incorporated into the proposed framework, using nonseparable Hamiltonians as an illustrative system class. We assess the method's performance based on the forecasting accuracy of a model estimated from-single trajectory data. We compare the Bayesian method to a state-of-the-art machine learning method on a canonical nonseparable Hamiltonian model and a chaotic double pendulum model with small, noisy training datasets. The results show that using the Bayesian posterior as a training objective can yield upwards of 724 times improvement in Hamiltonian mean squared error using training data with up to 10% multiplicative noise compared to a standard training objective. Lastly, we demonstrate the utility of the novel algorithm for parameter estimation of a 64-dimensional model of the spatially-discretized nonlinear Schr\"odinger equation with data corrupted by up to 20% multiplicative noise. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.12476 |
| رقم الأكسشن: | edsarx.2401.12476 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |