Research map / Probabilistic and scientific modeling / Differential equations and PDEs
DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes DISCO, a transformer hypernetwork that reads a short trajectory and generates the parameters of a small U-Net neural-ODE operator that is time-integrated to predict the next state, pretrained on PDEBench and The Well.
Problem
Predicting the next states of dynamical systems governed by unknown, varying temporal PDEs from only a short context trajectory, across different PDE classes, coefficients, and initial conditions.
Approach
Decouple dynamics estimation from state prediction: a large transformer hypernetwork infers the parameters of a much smaller convolutional U-Net operator from the context, which is then integrated with an adaptive Runge-Kutta solver, avoiding an autoencoder/decoder and preserving translation equivariance.
Key results
- On PDEBench next-step prediction, DISCO (300 epochs) reaches NRMSE 0.00056 on SWE and 0.0033 on INS, beating retrained MPP at 500 epochs (0.00075 and 0.0056).
- On The Well rollouts, DISCO achieves best NRMSE on most datasets, e.g., Gray-Scott t+1 0.00990 vs MPP 0.0652 and GEPS 0.158.
- On fine-tuning to unseen Euler equations, DISCO attains NRMSE 0.029 vs MPP 0.032, Poseidon 0.052, and UNet 0.050.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DISCO instead of MPP (retrained, 500 epochs) | PDEBench next-step prediction · Burgers | NRMSE: 0.0029 -> 0.0027 | Helped |
| Use DISCO instead of MPP (retrained, 500 epochs) | PDEBench next-step prediction · SWE | NRMSE: 0.00075 -> 0.00056 | Helped |
| Use DISCO instead of MPP (retrained, 500 epochs) | PDEBench next-step prediction · DiffRe2D | NRMSE: 0.0058 -> 0.0047 | Helped |
| Use DISCO instead of MPP (retrained, 500 epochs) | PDEBench next-step prediction · INS | NRMSE: 0.0056 -> 0.0033 | Helped |
| Use DISCO instead of MPP | PDEBench next-step prediction · CNS | NRMSE: 0.0227 -> 0.095 | Hurt |
| Use DISCO instead of MPP | Well rollout prediction · Gray-Scott reaction-diffusion, t+1 | NRMSE: 0.0652 -> 0.00990 | Helped |
| Use DISCO instead of MPP | Well rollout prediction · MHD, t+4 | NRMSE: 0.655 -> 0.684 | Mixed |
| Fine-tune pretrained DISCO on unseen Euler equations | DISCO · Euler equations (unseen physics) | NRMSE: 0.032 -> 0.029 | Helped |
| Reduce hypernetwork to 4 layers, 3 heads, dim 192 (ablation) | DISCO on DiffRe2D · DiffRe2D | NRMSE: 0.00133 -> 0.00211 | Hurt |
| Increase hypernetwork to 12 layers, 12 heads, dim 768 (ablation) | DISCO on DiffRe2D · DiffRe2D | NRMSE: 0.00133 -> 0.00203 | Hurt |
| Reduce operator c_start to 4 (ablation) | DISCO on DiffRe2D · DiffRe2D | NRMSE: 0.00133 -> 0.00330 | Hurt |
| Increase operator c_start to 12 (ablation) | DISCO on DiffRe2D · DiffRe2D | NRMSE: 0.00133 -> 0.000971 | Helped |
Surprising findings
- On the compressible Navier-Stokes dataset with coarse time resolution, DISCO does not reach MPP's performance in joint training (0.095 vs 0.037 at 300 epochs), though it beats MPP when trained alone.
- The GEPS-style meta-learning adaptation baseline performs poorly on multi-physics data (e.g., Rayleigh-Bénard and shear flow rollouts exceed NRMSE 1).
Limitations
- Assumes time-independent dynamics; extending to time-dependent systems is left for future work.
- Underperforms MPP on the compressible Navier-Stokes dataset in joint training due to coarse time resolution.
- Operator is convolutional on uniform grids, so non-uniform meshes or arbitrary geometries are not handled.
Experimental setup
Datasets: PDEBench The Well
Benchmarks: PDEBench The Well
Metrics: NRMSE
Baselines: MPP GEPS Poseidon U-Net FNO
Builds on: neural ODE MPP GEPS CODA Poseidon
Closest papers by meaning
- Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge (ICLR 2026 · similarity 0.90)
- Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators (NeurIPS 2026 · similarity 0.88)
- Learned Lagrangian Models of PDEs via Euler–Lagrange Residual Minimization (NeurIPS 2026 · similarity 0.87)
- Learning Physics Informed Neural ODEs with Partial Measurements (AAAI 2025 · similarity 0.87)
- Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning (NeurIPS 2024 · similarity 0.86)
- Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers (NeurIPS 2025 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.