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Physics-Informed Diffusion Models
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Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.
Forward citations
Cited by 8 Pith papers
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Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards
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Lantern: Conflict-Aware Gradient Blending for Physics-Guided Diffusion Models in Calorimeter Simulation
GradBlend anchors diffusion updates to denoising while admitting physics auxiliaries, improving calorimeter shower FPD and CFD where PCGrad, GradNorm, IMTL-G, and ConFIG inflate FPD by 2–100×.
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Physics-informed diffusion models in spectral space
A spectral-latent diffusion model with physics and observation guidance at inference solves forward and inverse PDE problems from sparse data with claimed large speedups.
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Integration Matters: Rollout-Based Training for Constrained Diffusion Models
Rollout-based fine-tuning with a learned adaptive guidance scaling yields near-zero constraint violations while preserving sample fidelity in constrained diffusion models.
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Generative Latent Diffusion Model for Inverse Modeling and Uncertainty Analysis in Geological Carbon Sequestration
A conditional neural field plus latent diffusion model jointly generates geological models and flow responses, enabling zero-shot Bayesian inversion for CO2 storage.
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Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series
A weighted physics-informed loss schedule during diffusion training improves unsupervised anomaly detection in multivariate time series, according to the paper's experiments.
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Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions
Feeding an S-DeepONet coarse prediction into a video diffusion model trained on the residual reduces PDE solution errors by 82% on cavity flow and 34% on plastic deformation, beating either single-stage model.
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Towards Digital Twins for Optimal Radioembolization
A review proposing a liver radioembolization digital twin that combines CFD with physics-informed neural networks to plan microsphere delivery.
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