Lorenz T. Biegler

Gul Hameed, Tao Chen, Antonio del Rio Chanona et al.

Gray-box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black-box models lacking analytic derivatives, remains a challenge. Trust-region (TR) methods provide a robust framework for gray-box problems through local reduced models (RMs) for black-box components, but they are complex and require extensive parameter tuning. Motivated by recent advances in funnel-based convergence theory for nonlinear optimization, we propose a novel TR funnel algorithm for gray-box optimization, replacing the filter acceptance criterion with a uni-dimensional funnel, maintaining a monotonically decreasing upper bound on approximation error of local black-box RMs. A global convergence proof to a first-order critical point is established. The algorithm, implemented open-source in Pyomo, supports multiple RM forms and globalization strategies (filter or funnel). Benchmark tests show the TR funnel algorithm achieves comparable and often improved performance relative to the classical TR filter method, thus providing a simpler, effective alternative for gray-box optimization.

Marcus J. Schytt, Lorenz T. Biegler, John B. Jørgensen

Power-to-ammonia (P2A) provides a carbon-free alternative to conventional ammonia production by replacing fossil-based feedstocks with electrolytic hydrogen and nitrogen from air separation. For decentralized P2A systems, pressure swing adsorption (PSA) offers a flexible alternative to cryogenic air separation. However, its industrial implementations are largely proprietary, and open, first-principles models capable of simulating its cyclic, nonlinear transport are scarce in literature. This work presents a first-principles, dynamic, one-dimensional model of a PSA superstructure for nitrogen generation, formulated with thermodynamically consistent equations of state, coupling multicomponent mass, energy, and momentum balances with kinetically limited adsorption on carbon molecular sieves. The resulting system of partial differential-algebraic equations (PDAEs) is semi-discretized using the finite volume method, integrated using diagonally implicit Runge-Kutta methods, and cyclic steady states (CSS) are computed via shooting-based solution methods. The framework is implemented in Julia, combining analytical derivatives with automatic differentiation and utilizing sparse linear algebra for efficient solution of the arising large nonlinear systems. The framework is demonstrated on a two-bed PSA cycle for air separation, comparing spatial and temporal discretization strategies, CSS solution methods, and the effects of ideal versus real-gas thermodynamics on predicted nitrogen purity and recovery. The proposed framework establishes an extensible basis for PSA simulation and optimization.

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.

Amir Patel, Stacey Shield, Saif Kazi et al.

In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with contacts employ mode-scheduling, which requires an a priori knowledge of the contact order and thus cannot produce complex or non-intuitive behaviors. Contact-implicit trajectory optimization methods offer a solution to this by allowing the optimization to make or break contacts as needed, but thus far have suffered from poor accuracy. Here, we combine methods from direct collocation using higher order orthogonal polynomials with contact-implicit optimization to generate trajectories with significantly improved accuracy. The key insight is to increase the order of the polynomial representation while maintaining the assumption that impact occurs over the duration of one finite element.