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Abstract Variational quantum eigensolvers (VQEs) represent a promising approach to computing molecular ground states and energies on modern quantum computers. These approaches use a classical computer to optimize the parameters of a trial wave function, while the quantum computer simulates the energy by preparing and measuring a set of bitstring observations, referred to as shots, over which an expected value is computed. Although more shots improve the accuracy of the expected ground state, it also increases the simulation cost. Hence, we propose modifications to the standard Bayesian optimization algorithm to leverage few‐shot circuit observations to solve VQEs with fewer quantum resources. We demonstrate the effectiveness of our proposed approach, Bayesian optimization with priors on surface topology (BOPT), by comparing optimizers for molecular systems and demonstrate how current quantum hardware can aid in finding ground‐state energies. 

Optimal design under uncertainty remains a fundamental challenge in advancing reliable, next-generation process systems. Robust optimization (RO) offers a principled approach by safeguarding against worst-case scenarios across a range of uncertain parameters. However, traditional RO methods typically require known problem structure, which limits their applicability to high-fidelity simulation environments. To overcome these limitations, recent work has explored robust Bayesian optimization (RBO) as a flexible alternative that can accommodate expensive, black-box objectives. Existing RBO methods, however, generally ignore available structural information and struggle to scale to high-dimensional settings. In this work, we introduce BONSAI (Bayesian Optimization of Network Systems under uncertAInty), a new RBO framework that leverages partial structural knowledge commonly available in simulation-based models. Instead of treating the objective as a monolithic black box, BONSAI represents it as a directed graph of interconnected white- and black-box components, allowing the algorithm to utilize intermediate information within the optimization process. We further propose a scalable Thompson sampling-based acquisition function tailored to the structured RO setting, which can be efficiently optimized using gradient-based methods. We evaluate BONSAI across a diverse set of synthetic and real-world case studies, including applications in process systems engineering. Compared to existing simulation-based RO algorithms, BONSAI consistently delivers more sample-efficient and higher-quality robust solutions, highlighting its practical advantages for uncertainty-aware design in complex engineering systems. 

Designing molecules that must satisfy multiple, often conflicting, objectives is a central challenge in molecular discovery. The enormous size of the chemical space and the cost of high-fidelity simulations have driven the development of machine learning-guided strategies for accelerating design with limited data. Among these, Bayesian optimization (BO) offers a principled framework for sample-efficient search, while generative models provide a mechanism to propose novel, diverse candidates beyond fixed libraries. However, existing methods that couple the two often rely on continuous latent spaces, which introduce both architectural entanglement and scalability challenges. This work introduces an alternative, modular “generate-then-optimize” framework for de novo multiobjective molecular design/discovery. At each iteration, a generative model is used to construct a large, diverse pool of candidate molecules, after which a novel acquisition function, qPMHI (multipoint Probability of Maximum Hypervolume Improvement), is used to optimally select a batch of candidates most likely to induce the largest Pareto front expansion. The key insight is that qPMHI decomposes additively, enabling exact, scalable batch selection via only a simple ranking of probabilities that can be easily estimated with Monte Carlo sampling. We benchmark the framework against state-of-the-art latent-space and discrete molecular optimization methods, demonstrating significant improvements across synthetic benchmarks and application-driven tasks. Specifically, in a case study related to sustainable energy storage, we show that our approach quickly uncovers novel, diverse, and high-performing organic (quinone-based) cathode materials for aqueous redox flow battery applications. 

The discovery of molecules with optimal functional properties is a central challenge across diverse fields such as energy storage, catalysis, and chemical sensing. However, molecular property optimization (MPO) remains difficult due to the combinatorial size of chemical space and the cost of acquiring property labels via simulations or wet-lab experiments. Bayesian optimization (BO) offers a principled framework for sample-efficient discovery in such settings, but its effectiveness depends critically on the quality of the molecular representation used to train the underlying probabilistic surrogate model. Existing approaches based on fingerprints, graphs, SMILES strings, or learned embeddings often struggle in low-data regimes due to high dimensionality or poorly structured latent spaces. Here, we introduce Molecular Descriptors with Actively Identified Subspaces (MolDAIS), a flexible molecular BO framework that adaptively identifies task-relevant subspaces within large descriptor libraries. Leveraging the sparse axis-aligned subspace (SAAS) prior introduced in recent BO literature, MolDAIS constructs parsimonious Gaussian process surrogate models that focus on task-relevant features as new data is acquired. In addition to validating this approach for descriptor-based MPO, we introduce two novel screening variants, which significantly reduce computational cost while preserving predictive accuracy and physical interpretability. We demonstrate that MolDAIS consistently outperforms state-of-the-art MPO methods across a suite of benchmark and real-world tasks, including single- and multi-objective optimization. Our results show that MolDAIS can identify near-optimal candidates from chemical libraries with over 100,000 molecules using fewer than 100 property evaluations, highlighting its promise as a practical tool for data-scarce molecular discovery. 

Symbolic regression (SR) is an emerging branch of machine learning focused on discovering simple and interpretable mathematical expressions from data. Although a wide-variety of SR methods have been developed, they often face challenges such as high computational cost, poor scalability with respect to the number of input dimensions, fragility to noise, and an inability to balance accuracy and complexity. This work introduces SyMANTIC, a novel SR algorithm that addresses these challenges. SyMANTIC efficiently identifies (potentially several) low-dimensional descriptors from a large set of candidates (from ∼105 to ∼1010 or more) through a unique combination of mutual information-based feature selection, adaptive feature expansion, and recursively applied l 0 -based sparse regression. In addition, it employs an information-theoretic measure to produce an approximate set of Pareto-optimal equations, each offering the best-found accuracy for a given complexity. Furthermore, our open-source implementation of SyMANTIC, built on the PyTorch ecosystem, facilitates easy installation and GPU acceleration. We demonstrate the effectiveness of SyMANTIC across a range of problems, including synthetic examples, scientific benchmarks, real-world material property predictions, and chaotic dynamical system identification from small datasets. Extensive comparisons show that SyMANTIC uncovers similar or more accurate models at a fraction of the cost of existing SR methods.