Conference Agenda

Graph neural networks (GNNs) have proven state-of-the-art performance in molecular property prediction tasks[1]. However, a significant challenge with GNNs is the reliability of their predictions, particularly in critical domains where quantifying model confidence is essential. Therefore, assessing uncertainty in GNN predictions is crucial to improving their robustness. Existing uncertainty quantification methods, such as Deep ensembles and Monte Carlo Dropout (MC-dropout), have been applied to GNNs with some success, but these methods are limited to approximate the full posterior distribution.

In this work, we propose a novel approach for scalable uncertainty quantification in molecular property prediction using Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) [2] with a cyclical learning rate. This method facilitates sampling from multiple posterior modes and improves posterior exploration within a single training round. Additionally, we compare the proposed methods with MC-dropout [3] and Deep ensembles [4], focusing on error analysis, calibration, and sharpness, considering both epistemic and aleatoric uncertainties. Our experimental results demonstrate that the proposed parallel-SGHMC approach significantly outperforms MC-dropout and Deep ensembles in terms of calibration and sharpness. Specifically, parallel-SGHMC reduces the sum of squared errors (SSE) by 99.4% and 75%, respectively, when compared to MC-dropout and Deep Ensembles. These findings suggest that parallel-SGHMC is a promising method for uncertainty quantification in GNN-based molecular property prediction.

[1] Schweidtmann, A. M., Rittig, J. G., Konig, A., Grohe, M., Mitsos, A., & Dahmen, M. (2020). Graph neural networks for prediction of fuel ignition quality. Energy & fuels, 34(9), 11395-11407.

[2] Chen, T., Fox, E., & Guestrin, C. (2014, June). Stochastic gradient hamiltonian monte carlo. In International conference on machine learning (pp. 1683-1691). PMLR.

[3] Gal, Y., & Ghahramani, Z. (2016, June). Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In international conference on machine learning (pp. 1050-1059). PMLR.

[4] Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30.

Reinforcement learning (RL)-driven process design methods [1-2] have received recent impetus, which strive to intelligently identify the optimal design solutions based on an available set of unit operations without any pre-postulation of superstructure or flowsheet configuration. This provides a more systematic and robust strategy to design optimal processes by minimizing the impact of prior expert knowledge. However, a key challenge for these methods lies in the significantly large combinatorial design space, which can be highly computationally intensive or even intractable to identify the truly optimal process design. To address the challenge, this work presents a novel approach integrating RL-driven design with quantum machine learning (QML). QML provides a promising alternative to expedite the design search, benefited from its theoretical speed advantages over their classical counterparts and the continuous advancement of real-world quantum machines [3-4]. Built on our prior work [5], the quantum-enhanced RL-driven approach starts with a maximum set of unit operations which are available for constructing the process design. Input-output stream matrix is used to represent the flowsheet structure, serving as the observation for reinforcement learning. A Deep Q-Network (DQN) algorithm is utilized to train a neural network (NN) as the RL agent to generate new flowsheet designs. Herein, the classical NN is replaced with a parameterized quantum circuit (PQC), a state-of-the-art model in QML that is considered the quantum equivalent of an NN [6-7]. The underlying principles and algorithm architecture of DQN are maintained to avoid model divergence and recent sampling bias when updating the PQC. The resulting designs are simulated and optimized using the python-based IDAES-PSE software [8]. The value of objective function (e.g., cost, productivity) is used as the reward to the agent toward continuously improving the design optimality. The efficacy and simulated computational tractability of this quantum-enhanced RL-driven process design algorithm will be demonstrated through a hydrodealkylation process case study. The key novelty of this work is to integrate two cutting-edge computing algorithms, QML and RL, aiming to provide an intelligent, efficient, and reliable approach toward automated process design.

References

[1] Stops, L.et al. (2023). Flowsheet generation through hierarchical reinforcement learning and graph neural networks. AIChE Journal, 69(1), e17938.

[2] Wang, D. et al. (2023). A coupled reinforcement learning and IDAES process modeling framework for automated conceptual design of energy and chemical systems. Energy Advances, 2(10), 1735-1751.

[3] Bernal, D. E. et al. (2022). Perspectives of quantum computing for chemical engineering. AIChE Journal, 68(6), e17651.

[4] Ajagekar, A. & You, F. (2022). New frontiers of quantum computing in chemical engineering. Korean Journal of Chemical Engineering, 39(4), 811–820.

[5] Tian, Y. et al. (2024). Reinforcement Learning-Driven Process Design: A Hydrodealkylation Example. 387–393.

[6] Jerbi, S. et al. (2021). Parametrized quantum policies for reinforcement learning (arXiv:2103.05577).

[7] Skolik, A. et al. (2022). Quantum agents in the Gym: A variational quantum algorithm for deep Q-learning. Quantum, 6, 720.

[8] Lee, A. et al. (2021). The IDAES process modeling framework and model library - Flexibility for process simulation and optimization. Journal of advanced manufacturing and processing, 3(3), e10095.

The complexity and demands of optimization problems are increasing due to economic and environmental constraints, as well as resource depletion. Combinatorial optimization (CO) is a critical area within optimization that holds significant importance in both academic and industrial contexts, with a variety of applications (Weinand et al., 2022). Despite recent advancements, solving CO problems remains challenging, primarily because of the growing problem size (NP-hard nature) and issues related to nonconvexity and bilinearity, which can result in multiple local solutions (Peres and Castelli, 2021). Numerous approaches have been suggested in literature to tackle these problems, utilizing classical methods, heuristics, and neural network (Blekos et al., 2024). However, these frequently fail to provide solutions or do so only within unrealistic timeframes, even for moderately sized problems (Pop et al., 2024).

To address these limitations, this work introduces an optimization approach based on quantum computing (QC). Over the past decade, QC has advanced rapidly and presents a promising technology for addressing CO problems that are intractable on classical hardware (Truger et al., 2024). This approach is advantageous due to its structural formulation.

In this work, the proposed framework employs quantum annealing (QA) to tackle CO problems through quantum adiabatic computation. As a case study, the Haverley’s pooling-blending problem (PBP) is presented and solved using both classical and quantum techniques. In applying the QA method to the PBP, the original problem is reformulated as a quadratic unconstrained binary optimization (QUBO) problem, expressed as minxQx^T, where x represents the binary decision variables and Q is a square matrix of constants. The transformation procedure involves several steps related to the transformation of the inequality constraints into equalities, the discretization of the continuous variables into binaries, the removal of bilinear terms, the introduction of quadratic penalty terms and the construction of the Q matrix. Furthermore, verbose and succinct transformations are employed, with the former expanding discretized variables for greater precision and the latter restricting them to integer values.

The resulting QUBO formulations are effectively embedded and solved, emerging as a promising solution technique. Specifically, QA exhibited the lowest computational time and the most consistent performance, indicating its suitability for embedding and solving this problem type. Moreover, verbose formulation required larger penalty multipliers compared to the succinct for all the examined solvers and the obtained results align with those previously reported in literature. The approach will be exposed in diverse numerical case studies to highlight its performance.

References

Blekos, K., et al. (2024). A review on quantum approximate optimization algorithm and its variants. Physics Reports, 1068, 1-66.

Peres, F., & Castelli, M. (2021). Combinatorial optimization problems and metaheuristics: Review, challenges, design, and development. Applied Sciences, 11(14), 6449.

Truger, F., et al. (2024). Warm-starting and quantum computing: A systematic mapping study. ACM Computing Surveys, 56(9), 1-31.

Weinand, J. M., et al. (2022). Research trends in combinatorial optimization. International Transactions in Operational Research, 29(2), 667-705.

Pop, P. C., et al. (2024). A comprehensive survey on the generalized traveling salesman problem. European Journal of Operational Research, 314(3), 819-835.