Sim+Real: Joint Simulation - Experiment Training Improves Balanced Prediction in Physical Systems

Simulation and experimental measurements provide complementary data for learning spatiotemporal physical systems, but standard simulation-to-experiment fine-tuning optimizes only the experimental objective after transfer and can degrade simulation performance. We formulate simulation--experiment prediction as a multi-objective learning problem with domain-specific simulation and experimental risks. On four fluid systems from RealPDEBench and two model capacities, we compare Simulation only, Experiment only, SimrightarrowExp, and Joint training, evaluating every final model on both held-out domains. SimrightarrowExp tends to specialize more strongly to experimental data at the cost of simulation-domain forgetting. Joint training consistently achieves the best balanced performance over a broad range of simulation--experiment evaluation weightings, while substantially improving simulation retention over SimrightarrowExp. Joint also better preserves simulation-only fields absent from experimental measurements. Project page: https://mahindrautela.github.io/morph.