Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gaussian, a Gaussian mixture generally has no closed-form expression for differential entropy and therefore requires numerical approximation. We propose a Gauss--Hermite quadrature method for evaluating Gaussian mixture differential entropy. The quadrature order controls the numerical resolution of the approximation. The method is evaluated on one- and two-dimensional Gaussian mixture benchmarks against Taylor approximations, analytic entropy bounds, and numerical integration references. For repeated optimization over continuous actions, we also propose a Hermite polynomial surrogate in action space. In a radar pointing benchmark, its second-order form achieves substantially lower surrogate error and optimizer regret than a second-order Taylor surrogate based on local derivatives at the nominal action, while both methods use nine direct objective evaluations per replanning step. The Hermite surrogate also improves pointing performance in the tested benchmark.
Fangnian Wang, Nicholas Tan Jerome, Thomas Jordan +1cs.NE cs.AI
Hydrogen infrastructure in enclosed environments, such as parking facilities for fuel cell vehicles, presents significant safety challenges due to hydrogen's low ignition energy and wide flammability range. Current monitoring systems are largely reactive, detecting leaks only after hazardous concentrations have formed. This study develops a computational framework for proactive sensor placement optimization by integrating computational fluid dynamics (CFD), genetic algorithm (GA) optimization, and a DeepSets neural surrogate. A CFD database of 180 scenarios was generated for a representative 50 m x 30 m x 3 m garage, covering multiple leak positions, rates (1-150 g/s), and ventilation conditions (ACH = 3-10 per hour). Sensor placement was optimized using a multi-objective GA and compared with uniform, random, and surrogate-assisted approaches. The GA achieved a detection rate of 96.1% within 60 s and reduced blind areas to 0.12%, corresponding to an approximately 5% improvement in composite fitness over a uniform baseline. The DeepSets surrogate reproduced near-optimal configurations with a fitness gap below 0.01 while reducing CFD evaluations by 89% and computational time by two orders of magnitude. Detection performance and spatial coverage remained comparable to the GA, demonstrating that surrogate-assisted optimization can retain solution quality while enabling rapid design iteration. Overall, the results show that CFD-informed optimization improves detection effectiveness and reduces sensor requirements compared to conventional layouts. The proposed framework supports scalable deployment and provides a foundation for integrating optimized sensor networks with digital twin systems for real-time monitoring and risk assessment.
Mohammad Haddadnia, Yuvan Chali, Abhilash Jayaraj +4cs.LG
Identifying high-utility candidates from massive discrete spaces under expensive evaluations is a recurring challenge across the sciences, with structure-based drug discovery as a prominent example. While surrogate-based optimization can increase sample efficiency by reducing the number of expensive evaluations, modern molecular libraries have reached billions to trillions of compounds, making full-library surrogate inference itself a major computational bottleneck. We introduce BOBa, a bandit-guided surrogate optimization framework that eliminates full-library inference by adaptively allocating computation across partitions of the action space. By treating partitions as arms in a multi-armed bandit, BOBa concentrates inference and evaluations on empirically promising partitions while maintaining principled exploration. Experiments on real-world synthesis-on-demand libraries demonstrate that optimism-under-uncertainty bandits, combined with meaningful action space partitioning, are essential for effective allocation of inference and evaluations. Our findings reveal a tunable tradeoff between screening performance and surrogate inference cost, which supports practical optimization over current libraries, and establishes a viable route to ultra-large library virtual screening.