A Multimodal Conditional Mixture Model with Distribution-Level Physics Priors

• URL: http://arxiv.org/abs/2602.10451v1
• Date: Wed, 11 Feb 2026 02:46:10 GMT
• Title: A Multimodal Conditional Mixture Model with Distribution-Level Physics Priors
• Authors: Jinkyo Han, Bahador Bahmani,
• Abstract summary: This work develops a physics-informed multimodal conditional modeling framework based on mixture density representations.<n>Physical knowledge is embedded through component-specific regularization terms that penalize violations of governing equations or physical laws.<n>The proposed framework is evaluated across a range of scientific problems in which multimodality arises from intrinsic physical mechanisms rather than observational noise.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many scientific and engineering systems exhibit intrinsically multimodal behavior arising from latent regime switching and non-unique physical mechanisms. In such settings, learning the full conditional distribution of admissible outcomes in a physically consistent and interpretable manner remains a challenge. While recent advances in machine learning have enabled powerful multimodal generative modeling, their integration with physics-constrained scientific modeling remains nontrivial, particularly when physical structure must be preserved or data are limited. This work develops a physics-informed multimodal conditional modeling framework based on mixture density representations. Mixture density networks (MDNs) provide an explicit and interpretable parameterization of multimodal conditional distributions. Physical knowledge is embedded through component-specific regularization terms that penalize violations of governing equations or physical laws. This formulation naturally accommodates non-uniqueness and stochasticity while remaining computationally efficient and amenable to conditioning on contextual inputs. The proposed framework is evaluated across a range of scientific problems in which multimodality arises from intrinsic physical mechanisms rather than observational noise, including bifurcation phenomena in nonlinear dynamical systems, stochastic partial differential equations, and atomistic-scale shock dynamics. In addition, the proposed method is compared with a conditional flow matching (CFM) model, a representative state-of-the-art generative modeling approach, demonstrating that MDNs can achieve competitive performance while offering a simpler and more interpretable formulation.

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