cs.LGAug 15, 2026

A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transients

Authors: Haoguang Wang, Huy Hoang Le, Akhila Kandivalasa, Christian Moya, Marcos Netto, Guang Lin

Organizations: School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA · R&D Department, Powermore Ltd., Da Nang, 550000 VN · Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102 USA · Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA

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Abstract

This paper proposes a Mamba surrogate model with mixture-of-experts (MoE) routing to represent the transient dynamics of inverter-based resources. A Mamba surrogate model is a predictive machine learning model built on the Mamba architecture. MoE routing uses a router network to assign data-dependent weights to specialized subnetworks (experts). The resulting Mamba--MoE surrogate can perform two tasks: (i) closed-loop simulation and (ii) measurement-window forecasting of inverter transients. A single Mamba backbone with task conditioning and expert routing serves both tasks, replacing two separate specialists. Task-matched objectives fit each prediction form, and an adaptive conformal layer provides prediction intervals for both tasks. For the considered grid-following inverter, the unified surrogate model remains in the same low-error regime as a Mamba specialist pair while using 13% fewer parameters. The prediction intervals achieve 94--96% empirical mean marginal coverage across the two tasks. For transient dynamics---that is, beyond the vicinity of an equilibrium point---our surrogate model with MoE routing yields lower errors across all outputs in both tasks compared to a shared Mamba backbone without expert routing. A controller hardware-in-the-loop simulation validates our results and shows that adapting only the shared output head with limited measured data reduces held-out forecasting error.

Figures & tables

Fig. 1: One-line diagram of the inverter–infinite-bus system. The inverter connects to the grid (modeled as an infinite bus) through a series rℓr\ell branch, with vˉcv=vcvejθcv\bar{v}^{\mathrm{cv}}=v^{\mathrm{cv}}e^{j\theta^{\mathrm{cv}}} and iˉcv=icvejαcv\bar{i}^{\mathrm{cv}}=i^{\mathrm{cv}}e^{j\alpha^{\mathrm{cv}}} .
Fig. 2: Task (i) closed-loop simulation; (ii) measurement-window forecasting, with HH outputs per forward pass and reported forecasting metrics based on h=1h{=}1 .
Fig. 3: The proposed Mamba–MoE surrogate architecture.
Fig. 4: Adaptive conformal calibration workflow.
ModelParamsOutputG-NRMSE Simulation (%)RMSE Simulation (pu)G-NRMSE Forecasting (%)RMSE Forecasting (pu)
Zero-delta—idcvi^{\mathrm{cv}}_{d}10.177.97×10−27.97\times 10^{-2}0.816.38×10−36.38\times 10^{-3}
iqcvi^{\mathrm{cv}}_{q}2.722.02×10−22.02\times 10^{-2}1.561.16×10−21.16\times 10^{-2}
irfilti_{r}^{\mathrm{filt}}10.187.97×10−27.97\times 10^{-2}0.816.38×10−36.38\times 10^{-3}
iifilti_{i}^{\mathrm{filt}}2.722.03×10−22.03\times 10^{-2}1.561.16×10−21.16\times 10^{-2}
DeepONet704,648idcvi^{\mathrm{cv}}_{d}0.191.53×10−31.53\times 10^{-3}0.107.59×10−47.59\times 10^{-4}
iqcvi^{\mathrm{cv}}_{q}1.481.10×10−21.10\times 10^{-2}1.421.06×10−21.06\times 10^{-2}
TABLE I: Clean-condition accuracy and parameter counts; baseline counts sum the parameters of the simulation and forecasting specialists.
VariantHeadKKFiLMλsim\lambda_{\mathrm{sim}}λfcast\lambda_{\mathrm{fcast}}OutputG-NRMSE SimulationRMSE SimulationG-NRMSE ForecastingRMSE Forecasting
       (%)(pu)(%)(pu)
Mamba–MoE Baseline1H4✓\checkmark1.01.0idcvi^{\mathrm{cv}}_{d}0.141.06×10−31.06\times 10^{-3}0.107.93×10−47.93\times 10^{-4}
iqcvi^{\mathrm{cv}}_{q}1.391.04×10−21.04\times 10^{-2}1.411.05×10−21.05\times 10^{-2}
irfilti_{r}^{\mathrm{filt}}0.211.64×10−31.64\times 10^{-3}0.129.70×10−49.70\times 10^{-4}
iifilti_{i}^{\mathrm{filt}}1.391.04×10−21.04\times 10^{-2}1.401.05×10−21.05\times 10^{-2}
(A) Two-head2H4✓\checkmark1.01.0idcvi^{\mathrm{cv}}_{d}0.151.15×10−31.15\times 10^{-3}0.032.60×10−42.60\times 10^{-4}
TABLE II: Ablation study on design components.
CategoryConditionOutputSimulationForecasting
BaselineCleanidcvi^{\mathrm{cv}}_{d}1.06×10−3/0.141.06{\times}10^{-3}/0.147.93×10−4/0.107.93{\times}10^{-4}/0.10
iqcvi^{\mathrm{cv}}_{q}1.04×10−2/1.391.04{\times}10^{-2}/1.391.05×10−2/1.411.05{\times}10^{-2}/1.41
irfilti_{r}^{\mathrm{filt}}1.64×10−3/0.211.64{\times}10^{-3}/0.219.70×10−4/0.129.70{\times}10^{-4}/0.12
iifilti_{i}^{\mathrm{filt}}1.04×10−2/1.391.04{\times}10^{-2}/1.391.05×10−2/1.401.05{\times}10^{-2}/1.40
Operating-point shiftΔpm ⁣× ⁣1.2\Delta p_{m}\!\times\!1.2 ( K=4K{=}4 )idcvi^{\mathrm{cv}}_{d}1.68×10−3/0.221.68{\times}10^{-3}/0.222.67×10−3/0.342.67{\times}10^{-3}/0.34
iqcvi^{\mathrm{cv}}_{q}2.69×10−2/3.622.69{\times}10^{-2}/3.622.72×10−2/3.652.72{\times}10^{-2}/3.65
TABLE III: Robustness under distribution shifts and measurement corruption. Entries are RMSE (pu) / G-NRMSE (%). Dashes (—) mark settings not evaluated; the sensor-dropout and measurement-noise tests are forecasting-only.
SetMethodidcvi^{\mathrm{cv}}_{d}iqcvi^{\mathrm{cv}}_{q}irfilti_{r}^{\mathrm{filt}}iifilti_{i}^{\mathrm{filt}}
IDPersistence2.233.012.163.15
ZS3.215.293.075.97
FT1.552.571.262.68
OOD-1Persistence1.181.721.161.52
ZS3.1116.324.8415.61
FT0.961.720.901.47
TABLE IV: Five-ms-ahead forecasting on the 9-bus system (target-set G-NRMSE, %).
Fig. 5: Simulation predictions with ACI intervals under a step disturbance.
Fig. 6: Forecasting predictions with ACI intervals.
Fig. 7: CHIL current forecasts before and after 10-s (5.1%) shared-output-head adaptation; the vertical reference line marks a DC-link-reference change.
MethodModeMean MCOV (%)Mean MPIW (pu)
CP (symmetric)Simulation91.700.005648
ACI (symmetric)Simulation94.470.004823
CP (symmetric)Forecasting94.550.002072
ACI (symmetric)Forecasting96.040.002255
TABLE V: ACI interval reliability.
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