Physics Foundation Models for Efficient Control of Fluid Flows

arXiv:2610.15173 · physics.flu-dyn, cs.LG · Submitted 2026-10-10 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Physics Foundation Models for Efficient Control of Fluid Flows".

Jane: The gist: A physics foundation model pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations,

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So to wrap up, this paper, "Physics Foundation Models for Efficient Control of Fluid Flows," investigates whether a physics foundation model pretrained for PDEs can be repurposed for closed-loop fluid-flow control by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations >

Jane: The core finding is that this approach works, achieving consistently higher reward while requiring smaller executed action magnitudes over training, which points toward improved control performance with reduced control effort >

Lu: This suggests that representations learned through self-supervised PDE forecasting can serve as an effective and parameter-efficient state-to-action control without needing task-specific backbone adaptation >

Meng: It shows that you can leverage pretraining on PDE dynamics for control tasks, even in a closed loop, by simply adding a lightweight actor and critic structure >

Tom: The authors did this by repurposing MORPH-Ti as the controller by removing its next-state decoder, pooling spatial representations, and attaching those control heads >

Jane: It really highlights how transfer of the representation itself—a backbone pretrained to model PDE dynamics—becomes the state encoder of an RL actor >

Lu: And it sets a precedent by showing that transferring a representation learned from one domain, like forecasting, to another domain, like control, can be done effectively >

Meng: For deployment at scale, the parameter efficiency is important; it trains only zero point one three four million parameters for the frozen MORPH controller compared to sixteen point six times and sixty-three point four times fewer than the MLP baseline >

Tom: So the main implication is that we can support effective and parameter-efficient state-to-action control without task-specific backbone adaptation >

Conclusion: Tom: So, we've been looking at this paper, "Physics Foundation Models for Efficient Control of Fluid Flows." Basically, it looks at taking a model that already understands how physical fluid equations work and using that knowledge to make a control policy for actual fluid flow.

Jane: And the main thing they show is you don't have to rewrite the whole control system from scratch. They take this physics foundation model and just attach some small actor and critic heads to it.

Lu: What I find interesting about that architecture is that you keep the heavy lifting—the representation learned from the PDE forecasting—completely frozen while you only train those new, lightweight heads for control.

Meng: That sounds good on paper, but what does that actually mean for deployment? Are we talking about something that runs smoothly in a real-world setting without needing massive retraining?

Tom: Well, the results are pretty compelling because they show that this frozen setup gets much better performance than a standard machine learning controller trained from scratch on all the raw data.

Jane: The numbers support that. At Reynolds number one hundred their frozen model was getting a reward around fifteen, while the baseline was stuck way lower, under five.

Lu: And what really stands out to me is how much smaller the action magnitudes get when you use this approach compared to the baseline. We saw it drop from about one point six down to maybe zero point three or four.

Tom: That reduction in control effort is huge for practical applications; it means less physical movement or energy needed to achieve the same result. It’s not just a better number on a score, it’s about efficiency.

Meng: Efficiency is key for us when we talk about shipping stuff to production because you want something that doesn't need constant babysitting or huge computational resources just to run the control loop.

Jane: So what this paper really suggests is that if you have a powerful representation already learned from physics, you can use it as the state encoder for control tasks without having to fundamentally change the underlying model structure.

Tom: Exactly. They’re saying these pre-learned physics representations are surprisingly good at capturing the necessary dynamics for fluid flow control.

Lu: It points toward a way where we can transfer knowledge learned from one type of simulation, like forecasting, directly into a completely different task like real-time control policy generation.

Meng: So, the implication is that we could be able to build much more compact and efficient controllers for complex physical systems using these foundation models.

Jane: And this leads us nicely into how these specific representations are structured and what kind of physics they’re actually encoding in the next segment.

Mahindra Rautela, Shaifalee Saxena, Alexander Scheinker

Los Alamos National Laboratory · University of New Mexico

physics.flu-dyn, cs.LG

Submitted: 2026-10-10

Updated: 2026-10-10

Project page: https://mahindrautela.github.io/morph

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

The gist: The gist: A physics foundation model pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control by attaching lightweight Gaussian actor and critic heads to frozen pretrained

Key concepts

Physics Foundation Model (PFM): A large AI model pre-trained on solving partial differential equations (PDEs), such as fluid flow simulations. This model learns the underlying physics of how fluids move and evolve over time, providing a rich, learned representation of the system's dynamics.
Frozen Representations: The core learned knowledge from the large PFM is kept unchanged during training for the control task. Only small, new components (the actor and critic heads) are trained to map these existing representations to desired control actions and value estimates.
Gaussian Actor/Critic Heads: Lightweight neural network heads attached to the frozen model. The actor generates the control action as a probability distribution (Gaussian), while the critic estimates the expected reward for a given state. These are trained specifically for fluid flow control.
Control Effort Reduction: The key finding is that using this repurposed PFM controller leads to much smaller executed actions compared to traditional methods. This means the model achieves better performance (higher reward) without needing large, disruptive physical inputs.

Terminology

Foundation Model — 1× in this paper · explained in 3 episodes
Foundation Models — 1× in this paper · explained in 7 episodes

Summary

The gist: A physics foundation model pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations, which achieves consistently higher reward while requiring smaller executed action magnitudes over training.

Repurposing the Foundation Model

The core investigation explores whether a physics foundation model (PFM) pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations The approach involves repurposing a pretrained physics foundation model, MORPH-Ti, as a flow-control policy by removing its next-state decoder, pooling the learned spatial representations, and attaching lightweight actor and critic heads The main comparison deliberately keeps the pretrained MORPH backbone frozen and trains only the actor and critic heads This study is the first to directly repurpose representations from a pretrained PDE foundation model as a closed-loop RL policy for fluid-flow control.

Control Adaptation and Architecture

The adaptation process involves bypassing the decoder of the MORPH model, mean-pooling the final-time tokens to obtain ht, and then attaching separate actor and value heads that parameterize a diagonal-Gaussian policy and scalar value function For MORPH-Ti, a real-space n × n scalar field is represented in UPTF-7 form with (B, T, F, C, D, H, W) = (B, 1, 1, 1, 1, n, n) for n ∈ two dimensions The final-time tokens are layer-normalized and mean-pooled to obtain ht ∈ R256 With frame normalization enabled, the raw spatial mean µSt and standard deviation σSt are appended, giving h˜t = [ht, µSt, σSt] ∈ R258 The actor is a lightweight MLP: 258 → 256 → 4 with a tanh hidden layer The critic has the corresponding structure.

Training and Comparison Setup

The comparison deliberately keeps the pretrained MORPH backbone frozen and trains only the actor/critic heads, contrasting it against a conventional PPO MLP that receives the same full-field vorticity observations All controllers are trained with proximal policy optimization (PPO) [Schulman et al., 2017], and shared optimization settings summarize the configuration used across resolutions and Reynolds numbers The PPO implementation alternates between collecting trajectories with the current policy and optimizing a clipped surrogate objective The comparison tests whether a representation learned entirely from PDE forecasting data can serve as a useful control encoder without downstream modification of the foundation model.

Experimental Results

At Re = 100, the frozen MORPH controller separates clearly from the full-field MLP baseline at both 64 × 64 and 128 × 128, with its reward rising to roughly 15 while the baseline remains below 5 Simultaneously, the mean executed action magnitude decreases from about 1.6 to approximately 0.35–0.4, whereas the baseline remains near 1.4–1.55 At Re = 200, the 64 × 64 frozen controller reaches a reward near 24 compared with roughly 16 for the matched baseline The corresponding action magnitudes decrease to roughly 0.95 and 0.65 for the frozen controllers, respectively, compared with about 1.7 for the 64×64 baseline. This indicates that the higher reward is not driven by a substantially different flow-energy state, but is instead associated primarily with a marked reduction in control effort.

Parameter Efficiency and Deployment

The frozen MORPH controller requires substantially fewer task-specific trainable parameters while reusing its frozen pretrained representation Table 2 highlights the parameter efficiency of the frozen MORPH controller, which trains only 0.134M parameters - 16.6× and 63.4× fewer than the MLP baseline at 64 × 64 and 128 × 128, respectively Rollouts further confirm stable long-closed-loop deployment across resolutions and flow regimes. The trajectories demonstrate that the learned policy can be deployed continuously in closed loop across different spatial resolutions and flow regimes while producing stable vorticity evolution over long horizon.

Conclusion

Pretrained PDE representations can support effective and parameter-efficient state-to-action control without task-specific backbone adaptation The results show that pretrained PDE representations can support effective and parameter-efficient state-to-action control without task-specific backbone adaptation >.

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