Carl D. Laird

Francesco Ceccon, Jordan Jalving, Joshua Haddad et al.

The optimization and machine learning toolkit (OMLT) is an open-source software package incorporating neural network and gradient-boosted tree surrogate models, which have been trained using machine learning, into larger optimization problems. We discuss the advances in optimization technology that made OMLT possible and show how OMLT seamlessly integrates with the algebraic modeling language Pyomo. We demonstrate how to use OMLT for solving decision-making problems in both computer science and engineering.

Laurens R. Lueg, Victor Alves, Daniel Schicksnus et al.

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has produced highly influential methods, such as neural ordinary differential equations (NODEs). Recent works extend this line of research to consider neural differential-algebraic systems of equations (DAEs), where some unknown relationships within the DAE are learned from data. Training neural DAEs, similarly to neural ODEs, is computationally expensive, as it requires the solution of a DAE for every parameter update. Further, the rigorous consideration of algebraic constraints is difficult within common deep learning training algorithms such as stochastic gradient descent. In this work, we apply the simultaneous approach to neural DAE problems, resulting in a fully discretized nonlinear optimization problem, which is solved to local optimality and simultaneously obtains the neural network parameters and the solution to the corresponding DAE. We extend recent work demonstrating the simultaneous approach for neural ODEs, by presenting a general framework to solve neural DAEs, with explicit consideration of hybrid models, where some components of the DAE are known, e.g. physics-informed constraints. Furthermore, we present a general strategy for improving the performance and convergence of the nonlinear programming solver, based on solving an auxiliary problem for initialization and approximating Hessian terms. We achieve promising results in terms of accuracy, model generalizability and computational cost, across different problem settings such as sparse data, unobserved states and multiple trajectories. Lastly, we provide several promising future directions to improve the scalability and robustness of our approach.

Daniel Ovalle, Lorenz T. Biegler, Ignacio E. Grossmann et al.

We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible. This guarantee holds with probability at least $1{-}α$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.