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

Mahindra Rautela; Alexander Scheinker; Ayan Biswas; Diane Oyen; Nathan DeBardeleben; Earl Lawrence

cs.LGOct 1, 2026

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

Authors: Mahindra Rautela, Alexander Scheinker, Ayan Biswas, Diane Oyen, Nathan DeBardeleben, Earl Lawrence

Organizations: Los Alamos National Laboratory, New Mexico, USA

Abstract

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, Sim $\rightarrow$ Exp, and Joint training, evaluating every final model on both held-out domains. Sim $\rightarrow$ Exp 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 Sim $\rightarrow$ Exp. Joint also better preserves simulation-only fields absent from experimental measurements. Project page: https://mahindrautela.github.io/morph.

Figures & tables

Dataset	Sim. fields	Exp. fields	Sim. grid	Exp. grid
Cylinder	$u,v,p$	$u,v$	$64\!\times\!128$	$128\!\times\!256$
Controlled Cylinder	$u,v,p$	$u,v$	$64\!\times\!128$	$128\!\times\!256$
FSI	$u,v,p$	$u,v$	$128\!\times\!128$	$128\!\times\!128$
Foil	$u,v,p$	$u,v$	$128\!\times\!256$	$128\!\times\!256$

Table 1: RealPDEBench systems. The four fluid datasets share velocity observables

(u,v)

; simulation additionally contains pressure. The grids shown are the native benchmark grids.

		Simulation only			Experiment only			Sim $\rightarrow$ Exp			Joint
Dataset	Capacity	bRMSE	bRelL2	bfRMSE	bRMSE	bRelL2	bfRMSE	bRMSE	bRelL2	bfRMSE	bRMSE	bRelL2	bfRMSE
Cylinder	17.5M	0.118098	0.539958	0.019925	0.101539	0.332502	0.015969	0.100507	0.419261	0.015714	0.058412	0.126032	0.009489
Cylinder	48.2M	0.096126	0.427966	0.015923	0.094315	0.311948	0.014704	0.094171	0.354185	0.014653	0.056230	0.098416	0.009077
Ctrl Cyl	17.5M	0.049899	0.333784	0.012611	0.061036	0.405474	0.014763	0.071465	0.490167	0.017985	0.030442	0.216437	0.006148
Ctrl Cyl	48.2M	0.048514	0.298634	0.012441	0.058852	0.393601	0.014363	0.077844	0.481965	0.019656	0.020455	0.149020	0.004180
FSI	17.5M	0.060337	0.405078	0.009692	0.082525	0.463016	0.013427	0.069920	0.392799	0.010924	0.033517	0.229200	0.004630

Table 2: Main result: balanced dual-domain performance on the four fluid datasets. bRMSE, bRelL2, and bfRMSE give simulation and experiment equal weight according to Eq. ( 1 ). Lower is better. Bold marks the best protocol for each dataset and model capacity. Joint is best in all 24 comparisons (8 settings

\times

3 metrics).

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Input frames	Target frames	Mask probability	Noise scale
Cylinder	20	20	0.1	0.1
Controlled Cylinder	10	10	0.1	0.1
FSI	20	20	0.5	0.1
Foil	20	20	0.1	0.1

Appendix

Table 3: Dataset-specific temporal and numerical-training settings used by the final runs. Masking and noise are applied only by the RealPDEBench numerical training dataset; validation, test, experimental training, and normalization data are clean.

Architecture	Variable grid	Variable field set	Field-wise cross-attention	Selected
Vanilla ViT [ Dosovitskiy et al., 2021 ]	Partial	No	No	No
U-Net [ Ronneberger et al., 2015 ]	Partial	No	No	No
FNO [ Li et al., 2020b ]	Yes	No	No	No
DPOT [ Hao et al., 2024 ]	Partial	Partial	No	No
Poseidon [ Herde et al., 2024 ]	Yes	Partial	No	No
Walrus [ McCabe et al., 2025 ]	Yes	Partial	No	No

Appendix

Table 4: Capability-based architecture selection for heterogeneous simulation–experiment training. “Partial” denotes that padding, interpolation, resizing, or task-specific interfaces are required in the standard formulation. The table compares interface capabilities rather than predictive accuracy.

Configuration	Parameters	Conv. filters	Latent dim.	Heads	Depth	MLP dim.
Ti	17,528,776	8	256	4	4	1024
S	48,161,736	8	512	8	4	2048

Appendix

Table 5: Architecture configurations used in the controlled study. Parameter counts are the trainable counts of the instantiated models.

Setting	Value
Optimizer	Adam
Learning rate	$10^{-4}$
Weight decay	0
Scheduler	cosine annealing to zero, $T_{\mathrm{max}}=10{,}000$ per stage
Stage budget	10,000 optimizer updates
Physical train batch size	6 (Cylinder, Controlled Cylinder, FSI); 3 (Foil)

Appendix

Table 6: Optimization settings used in the final runs. The physical training batch size is dataset-specific but fixed across protocols within each dataset.

Protocol	Optimizer steps	Sim. batches	Exp. batches	Stage structure
Simulation only	10,000	10,000	0	one simulation stage
Experiment only	10,000	0	10,000	one experimental stage
Sim $\rightarrow$ Exp	20,000	10,000	10,000	10k sim $+$ 10k exp
Joint	10,000	10,000	10,000	paired losses before each step

Appendix

Table 7: Optimizer-step and source-exposure budgets. Within each dataset, Joint and Sim

\rightarrow

Exp are matched in source-specific mini-batch and sample exposure and in forward/backward evaluations, but not in optimizer-step count.

				Simulation test			Experimental test
Dataset	Model	Params.	Training	RMSE $\downarrow$	Rel. $L_{2}$ $\downarrow$	fRMSE $\downarrow$	RMSE $\downarrow$	Rel. $L_{2}$ $\downarrow$	fRMSE $\downarrow$
Cylinder	MORPH-Ti	17.5M	Simulation only	0.014863	0.089989	0.002119	0.166353	0.989927	0.028099
			Experiment only	0.108947	0.551503	0.017663	0.093546	0.113501	0.014074
			Sim $\rightarrow$ Exp	0.105315	0.730744	0.017025	0.095457	0.107778	0.014283
			Joint	0.017445	0.107683	0.002650	0.080744	0.144381	0.013156
	MORPH-S	48.2M	Simulation only	0.015774	0.085703	0.002150	0.135024	0.770230	0.022416

Appendix

Table 8: Full dual-domain test performance on the four fluid datasets. Both simulation and experimental metrics are computed on the shared velocity fields

(u,v)

. Lower is better. Bold marks the best protocol for each model capacity, test domain, and metric. Results are seed 0.

Figure 1: Cylinder: sensitivity to simulation–experiment evaluation weighting. Rows show MORPH-Ti and MORPH-S and columns show RMSE, relative $L_{2}$ , and fRMSE (lower is better). Here, $\lambda=0$ weights only experimental performance and $\lambda=1$ only simulation performance; $\lambda=0.5$ recovers the balanced metrics in Table 2 . Joint gives the lowest error for all three metrics and both capacities throughout $\lambda=0.1$ – $0.9$ . At the single-domain endpoints, Sim $\rightarrow$ Exp is lowest only for experimental relative $L_{2}$ , while Simulation only becomes best for MORPH-Ti at $\lambda=1$ ; Joint remains best for MORPH-S.

Figure 2: Controlled Cylinder: sensitivity to simulation–experiment evaluation weighting. Rows show MORPH-Ti and MORPH-S and columns show RMSE, relative $L_{2}$ , and fRMSE (lower is better). Joint gives the lowest error for all three metrics and both capacities throughout $\lambda=0.1$ – $0.9$ . Sim $\rightarrow$ Exp is best at the purely experimental endpoint ( $\lambda=0$ ), whereas at $\lambda=1$ Simulation only gives the lowest RMSE and Joint retains the lowest relative $L_{2}$ and fRMSE.

Figure 3: Foil: sensitivity to simulation–experiment evaluation weighting. Rows show MORPH-Ti and MORPH-S and columns show RMSE, relative $L_{2}$ , and fRMSE (lower is better). Joint gives the lowest error for all three metrics over $\lambda=0.1$ – $0.9$ for MORPH-Ti and $\lambda=0.1$ – $0.8$ for MORPH-S. Sim $\rightarrow$ Exp is best at the purely experimental endpoint ( $\lambda=0$ ), while Simulation only becomes best near the purely simulation endpoint, at $\lambda=1$ for MORPH-Ti and $\lambda\geq 0.9$ for MORPH-S.

Figure 4: FSI: sensitivity to simulation–experiment evaluation weighting. Rows show MORPH-Ti and MORPH-S and columns show RMSE, relative $L_{2}$ , and fRMSE (lower is better). Joint gives the lowest error for all three metrics and both capacities throughout $\lambda=0.2$ – $0.9$ . At $\lambda=0.1$ , Joint remains best for RMSE and fRMSE while Sim $\rightarrow$ Exp has the lowest relative $L_{2}$ . Sim $\rightarrow$ Exp is best at $\lambda=0$ ; at $\lambda=1$ , Simulation only is best for MORPH-Ti, whereas Joint remains best for MORPH-S.

		Sim $\rightarrow$ Exp			Joint			RMSE reduction (%) $\uparrow$
Dataset	Model	RMSE $\downarrow$	Rel. $L_{2}$ $\downarrow$	fRMSE $\downarrow$	RMSE $\downarrow$	Rel. $L_{2}$ $\downarrow$	fRMSE $\downarrow$	RMSE reduction (%) $\uparrow$
Cylinder	MORPH-Ti	0.292374	0.973175	0.050192	0.055293	0.179063	0.008347	81.1
Cylinder	MORPH-S	0.261182	0.869020	0.040659	0.034885	0.112863	0.005319	86.6
Controlled Cylinder	MORPH-Ti	0.262821	0.716707	0.067997	0.116303	0.315430	0.023091	55.7
Controlled Cylinder	MORPH-S	0.225042	0.613608	0.050295	0.071026	0.192083	0.013899	68.4
FSI	MORPH-Ti	0.661982	0.947801	0.102268	0.270900	0.400808	0.042135	59.1

Appendix

Table 9: Numerical-pressure retention after experimental adaptation. Pressure

p

is supervised in simulation but is unavailable in the experimental measurements. The table therefore focuses on Sim

\rightarrow

Exp and Joint. Experiment only is not reported because pressure is never supervised in that protocol. Lower is better for the error metrics. The final column reports the percentage reduction in pressure RMSE achieved by Joint relative to Sim

\rightarrow

Exp,

100(E_{\mathrm{Sim\rightarrow Exp}}-E_{\mathrm{Joint}})/E_{\mathrm{Sim\rightarrow Exp}}

. Joint is lower than Sim

\rightarrow

Exp in all 24 metric comparisons (8 settings

\times

3 metrics).

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