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DiffPhyCon: A Generative Approach to Control Complex Physical Systems
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Proposes DiffPhyCon, a diffusion-based energy-optimization method that jointly generates state trajectories and control sequences under a control objective, with a prior-reweighting term (gamma) to find controls beyond the training distribution, and releases a jellyfish CFD dataset as a benchmark.
Problem
Controlling complex physical systems over long horizons requires optimizing control sequences that stay faithful to system dynamics and often lie far outside the training distribution; existing SL, RL, PID and MPC methods suffer from myopic failures, adversarial trajectories, or high cost.
Approach
Treat the joint trajectory-and-control sequence as one variable modeled by a diffusion model (learned energy), and optimize it jointly with the control objective during sampling; decompose the energy into a control-sequence prior and a conditional trajectory term, then reweight the prior with exponent gamma (gamma<1 flattens it) to escape the training distribution.
Key results
- On 1D Burgers' control, DiffPhyCon reduces control error vs best baseline by 30.1%, 52.6%, and 44.6% in PO-FC, FO-PC, PO-PC settings.
- On jellyfish full observation, DiffPhyCon reaches control objective -74.11 vs best baseline BPPO -20.93 and average speed 279.87 vs 107.67.
- On 2D smoke control, DiffPhyCon achieves J=0.2254 vs best baseline BPPO 0.3066.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DiffPhyCon instead of the strongest reported baseline | 1D Burgers' equation control · PO-FC | control error: 0.01577 -> 0.01103 | Helped |
| Use DiffPhyCon instead of the strongest reported baseline | 1D Burgers' equation control · FO-PC | control error: 0.00078 -> 0.00037 | Helped |
| Use DiffPhyCon instead of the strongest reported baseline | 1D Burgers' equation control · PO-PC | control error: 0.00891 -> 0.00494 | Helped |
| Add prior reweighting (rather than using γ=1) (ablation) | DiffPhyCon-lite on 1D Burgers' equation · PO-FC | control error: 0.01139 -> 0.01103 | Helped |
| Add prior reweighting (rather than using γ=1) (ablation) | DiffPhyCon-lite on 1D Burgers' equation · FO-PC and PO-PC | control error: 0.00037 -> 0.00037; 0.00494 -> 0.00494 | No clear effect |
| Add prior reweighting (rather than using γ=1) (ablation) | DiffPhyCon-lite on 2D jellyfish control · Full and partial observation | control objective: -20.47 -> -74.11; 74.97 -> -23.32 | Helped |
| Add prior reweighting (rather than using γ=1) (ablation) | DiffPhyCon-lite on 2D smoke indirect control · 2D smoke indirect control | control objective: 0.2324 -> 0.2254 | Helped |
| Use DiffPhyCon instead of the strongest reported baseline | 2D jellyfish control · Full observation | control objective: -20.93 -> -74.11 | Helped |
| Use DiffPhyCon instead of the strongest reported baseline | 2D jellyfish control · Partial observation | control objective: -3.02 -> -23.32 | Helped |
| Use DiffPhyCon instead of the strongest reported baseline | 2D smoke indirect control · 2D smoke indirect control | control objective: 0.3066 -> 0.2254 | Helped |
Surprising findings
- Generated jellyfish control sequences show a fast-close-slow-open pattern that is rare in training data but aligns with fluid dynamics findings.
- DiffPhyCon-lite (no prior reweighting) performs nearly as well as full DiffPhyCon on Burgers tasks, since the conditional prior already determines the optimum.
Limitations
- Prior reweighting with gamma requires training and evaluating an additional prior model, increasing cost.
- Partial-observation and partial-control settings rely on zero-padding and assumptions about which regions are controllable.
Experimental setup
Datasets: 1D Burgers' equation simulations (finite difference solver) Jellyfish movement dataset (Lily-Pad simulator) 2D smoke control dataset
Benchmarks: 1D Burgers' equation control (PO-FC, FO-PC, PO-PC) 2D jellyfish movement control (full and partial observation) 2D smoke indirect control
Metrics: control error J_control average speed control energy R(w) control objective J
Baselines: PID MPC SL SAC (offline) SAC (surrogate-solver) BC BPPO
Builds on: DDPM classifier guidance Lily-Pad simulator Behavior Proximal Policy Optimization
Closest papers by meaning
- CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systems (ICLR 2025 · similarity 0.90)
- DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learning (NeurIPS 2024 · similarity 0.85)
- A Differential and Pointwise Control Approach to Reinforcement Learning (NeurIPS 2025 · similarity 0.85)
- Safe and Stable Control via Lyapunov-Guided Diffusion Models (NeurIPS 2025 · similarity 0.85)
- Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence (ICML 2025 · similarity 0.85)
- One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillation (ICML 2025 · similarity 0.85)
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