Tongjia Liu | Searcharxiv

arXiv2026

Symbolic Discovery of Iterative Algorithms: A Continuous Latent Space Bayesian Optimization Framework

In this paper, we consider the automated discovery of iterative optimization algorithms. We formulate the algorithm discovery task as a discrete optimization problem and search for new update functions using latent space Bayesian Optimization. The proposed framework first learns a continuous representation of the discrete space of update functions using variational autoencoders, transforming the algorithm discovery task from a discrete to a continuous search problem. The continuous representation is subsequently used to search for new algorithms using Bayesian optimization. Application to two case studies shows that the proposed approach can discover new update functions in symbolic form without any assumptions on the functional form of the update function. Moreover, the computational time required to discover the new update functions is lower than existing mathematical programming-based approaches.

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arXiv2026

Learning regime-dependent governing equations: A symbolic decision tree approach

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We propose symbolic decision trees for the data-driven discovery of regime-dependent governing equations. The method simultaneously learns interpretable splitting conditions to partition the input domain and local governing equations that describe each regime. To improve tractability, both the splitting conditions and governing equations are parametrized using basis functions, resulting in a mixed-integer optimization learning problem. We use the proposed approach to learn hybrid dynamical models and a constitutive equation for the zero-shear viscosity of polymer melts. Symbolic decision trees identify physically interpretable regimes and local governing equations while improving predictive accuracy relative to approaches that learn a single global model or use existing decision tree models. This framework provides an interpretable and generalizable route for discovering regime-dependent models in chemical engineering systems.

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