Generating Physical Dynamics under Priors
Zihan Zhou, Xiaoxue Wang, Tianshu Yu
TL;DR
This paper presents a novel diffusion-based generative framework that incorporates physical priors, such as invariance and conservation laws, to produce realistic and physically consistent dynamics in a data-driven manner.
Contribution
It introduces a new method that seamlessly embeds physical priors into generative models, improving the physical realism of generated dynamics.
Findings
Produces high-quality, physically realistic dynamics across various phenomena
Demonstrates robustness and adherence to physical laws in generated trajectories
Advances data-driven modeling in physics with improved physical consistency
Abstract
Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and suboptimal performance. In this paper, we introduce a novel framework that seamlessly incorporates physical priors into diffusion-based generative models to address this limitation. Our approach leverages two categories of priors: 1) distributional priors, such as roto-translational invariance, and 2) physical feasibility priors, including energy and momentum conservation laws and PDE constraints. By embedding these priors into the generative process, our method can efficiently generate physically realistic dynamics, encompassing trajectories and flows. Empirical evaluations demonstrate that our…
Peer Reviews
Decision·ICLR 2025 Poster
1. The manuscript is well-written and easy to follow. 2. Thorough derivations are provided in the main content and appendix. 3. Sufficient experiments and ablation studies are conducted to validate the effectiveness of the proposed method.
Please see the Question part.
- The work is innovative in its focus on embedding physical feasibility directly into diffusion-based generative models, specifically through the use of both distributional and physical priors. By designing a process that enforces these constraints, the model is capable of generating realistic dynamics, distinguishing it from more traditional generative approaches that may ignore or only partially enforce physical laws. - Moreover, the paper is well-written and is thorough with both the theoret
- The experiments focus on synthetic datasets or physics-inspired datasets, and while this is valuable, additional testing on real-world, noisy datasets would definitely help. - If possible, comparing the model's performance with more baselines will make the empirical results more convincing. Yet it might be difficult to find the methods from the exactly same field, but some methods from, e.g. time-series forecasting, can be taken into consideration.
1. **Relevant topic.** There is increased interest in the dynamical system modelling community to incorporate relevant priors into models. Not only would this help with more efficient training, but perhaps more importantly, it should lead to better stability and capabilities to generalise out-of-distribution (OOD - when the test data comes from a different distribution than the training data). 2. **Wide range of datasets.** The experiments are performed on a wide range of datasets - four PDE one
1. **Contribution in distributional prior incorporation.** I believe there is some related work that is not being mentioned in section 3.1, as there are now plenty of works studying the incorporation of relevant priors in diffusion models. For example, Mathieu et al. [1] incorporate a series of geometric priors in infinite-dimensional modelling, also focusing on conditions for the diffusion process to be G-invariant assuming that the score network is G-equivariant. 2. **Lack of empirical evidenc
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Computational Physics and Python Applications