Summary of Bayesian Identification Of Nonseparable Hamiltonians with Multiplicative Noise Using Deep Learning and Reduced-order Modeling, by Nicholas Galioto et al.
Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling
by Nicholas Galioto, Harsh Sharma, Boris Kramer, Alex Arkady Gorodetsky
First submitted to arxiv on: 23 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Dynamical Systems (math.DS); Data Analysis, Statistics and Probability (physics.data-an); Computation (stat.CO)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a Bayesian approach to learn nonseparable Hamiltonian systems, which can be applied to high-dimensional systems and noisy data. The method is composed of three parts: (1) a Gaussian filter for evaluating the likelihood in the Bayesian posterior, (2) an algorithm for cost-effective Bayesian system identification, and (3) incorporation of structure-preserving methods using nonseparable Hamiltonians as an example. The approach is demonstrated on various models, including a canonical nonseparable Hamiltonian model and a chaotic double pendulum model with small noisy training datasets. The results show that the Bayesian method outperforms state-of-the-art machine learning approaches in forecasting accuracy. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us learn about complex systems using math and computers. Scientists often want to understand these systems, but they can be very hard to study because of noise or uncertainty. To make it easier, this paper introduces a new way to use Bayesian models, which are like super-smart calculators that can handle lots of data and noise. This approach is good for learning about big systems with many parts, and it’s tested on some examples. The results show that this method can be really helpful in predicting what will happen next, even when the data is noisy. |
Keywords
* Artificial intelligence * Likelihood * Machine learning
