Reduced-Order State Estimation of Fluid Flows via Diffusion-Augmented Particle Filtering

  • Tran, Jonathan (University of California, Los Angeles)
  • Eldredge, Jeff (University of California, Los Angeles)
  • Taira, Kunihiko (University of California, Los Angeles)

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In the mechanical sciences, classical approaches to state estimation and data assimilation may struggle in scenarios with high-dimensionality, non-Gaussianity, and nonlinearity [1]. For these problems, diffusion models serve as a promising avenue due to their flexibility in representing complex data distributions as well as their straightforward interpretation as a nonequilibrium thermodynamic system [2,3,4]. In this work, we present a reduced-order framework that leverages autoencoder-based manifold learning combined with score-based diffusion models and particle filtering to perform probabilistic state estimation and Bayesian data assimilation in a tractable manner. This diffusion model–based formulation extends recent Kalman-filter-based latent sequential filtering approaches in [6] by utilizing learned, nonparametric representations of the instantaneous state distribution. As a demonstrative example, we consider gust-airfoil interactions, characterized by massive separation, unsteadiness, and nonlinearity [7]. State estimation from sparse sensor measurements is framed as a probabilistic inverse problem, which is solved using a conditional score-based diffusion model. Rather than learning the distribution of the instantaneous state directly in the high-dimensional physical state space, we infer the distribution of its pushforward probability measure on a low-dimensional latent manifold identified by an autoencoder network. To propagate the latent probability distributions in time, the continuous-time flow field dynamics are approximated by a neural ODE surrogate model, which evolves trajectories on the latent space manifold. To facilitate sequential assimilation of sensor measurements, we employ a particle filter-based approach using likelihood estimates from the low-dimensional latent state and mitigate covariance collapse by constructing an empirical bootstrapped posterior augmented with samples from the diffusion model. By working in a reduced latent space, the proposed framework enables tractable state estimation while remaining agnostic to non-Gaussian distributions and nonlinear system dynamics.