Bandit Neural Architecture Search for Digital Twin Optimisation: A Scientific Machine Learning Approach

The successful deployment of Digital Twins for real-time optimisation of physical systems relies critically on highly accurate and efficient deep learning surrogate models. Ensuring these models meet performance and latency requirements demands rigorous Neural Architecture Search (NAS) and Hyperparameter Optimisation (HPO). While both have been traditionally posed as a pure-exploration bandit problem, we show that it fails to capture the unique, deterministic characteristics of Scientific Machine Learning (SciML) models underpinning Digital Twins, particularly Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). We propose a non-stochastic multi-armed bandit with balanced exploration-exploitation as the proper setting for Neural Architecture Search in Scientific Machine Learning and introduce BanditNAS, a novel algorithm that addresses three critical challenges absent from current approaches: (i) late convergence in high-capacity models exhibiting spectral bias, (ii) validation loss plateaus requiring optimiser switching, and (iii) the deterministic (non-stochastic) nature of physics-based training data. We analyse BanditNAS ’s theoretical properties, proving improved regret bounds compared to adaptive adversaries, and compare it empirically with state-of-the-art approaches across three representative SciML scenarios. Our results demonstrate setting-dependent performance: BanditNAS achieves up to \ (95\%\) higher optimal selection rates when multi-stage fine-tuning is required (DeepONets with L-BFGS switching), approximately \ (50\%\) improvement in late-convergence regimes (high-capacity PINNs), and comparable performance to HyperBand in moderately noisy environments, though underperforming in very large search spaces with high noise (\ (K=200\) graph networks). Statistical significance testing confirms BanditNAS ’s superiority in two of three settings (\ (p<0. 001\) ), with competitive performance in the third when restricted to \ (K 100\). These findings establish BanditNAS as a viable and theoretically grounded approach for optimising SciML models where real-time accuracy, multi-stage training, and computational resource constraints are paramount, while highlighting the importance of algorithm selection based on problem characteristics.