Scientific ML: PDEs & Neural Operators

Semi-Supervised Neural Operator Learning for Parameter-Scarce Trajectories

Barrier to removePartly addressed

Possible candidate · 2/5 runs4 papers report this75% from 2025+

Generated automatically from the limitations stated in 4 papers (ICML, CVPR, NeurIPS), listed under Evidence. It is not a paper, and it does not come from papers submitted to CSPaper.

The problem

Existing neural operators and trajectory surrogate models for continuum mechanics require dense, ground-truth physical parameter labels for every training trajectory. In experimental and real-world physical systems, recording state trajectories is feasible, but measuring underlying continuum or constitutive parameters is often costly, destructive, or impossible. Because existing methods lack semi-supervised formulations, they cannot leverage unlabeled experimental trajectories and remain restricted to fully labeled synthetic simulations.

Why it matters

Enables learning neural operators and physics surrogates directly from real-world trajectory observations where ground-truth material or system parameters are known for only a small subset of runs.

Ways to approach it

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1
Implement a semi-supervised pseudo-labeling framework using an inverse model to estimate parameters on unlabeled trajectories, measuring rollout RMSE and parameter recovery error across label fractions (5% to 50%) on standard PDE and MPM trajectory benchmarks.
2
Design a trajectory-consistency regularization objective based on physical symmetries and temporal sub-sampling on unlabeled trajectories, measuring sample-efficiency scaling curves compared to fully supervised baselines.
3
Test sim-to-real adaptation by training on parameter-labeled synthetic trajectories combined with unlabeled real/experimental physical trajectories, measuring rollout prediction error on held-out physical sequences.

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Why it might fail

If the mapping from state trajectories to physical parameters is severely non-unique or ill-conditioned, pseudo-labeling will amplify parameter errors and cause the forward operator's autoregressive rollouts to diverge.

Evidence

Each paper's own statement of the limitation, verbatim.

Zebra: In-Context Generative Pretraining for Solving Parametric PDEsICML 2025
Requires a large number of training trajectories with substantial parameter-space diversity; unsuited to data-scarce regimes.
UniPhy: Learning a Unified Constitutive Model for Inverse Physics SimulationCVPR 2025
Trained and evaluated only on simulated MPM trajectories; no real-world visual/physical data demonstrated
RIGNO: A Graph-based Framework For Robust And Accurate Operator Learning For PDEs On Arbitrary DomainsNeurIPS 2025
Requires a large number of training samples to reach small error (e.g., 1024 trajectories), as evidenced by scaling curves; no theoretical approximation or generalization guarantees
Disentangled Generative Models for Robust Prediction of System DynamicsICML 2023
Requires ground-truth parameter labels for every training trajectory, which is costly and mostly unavailable outside simulation; authors note semi-supervised extension is needed for real-world use