arXiv subjects

Joshua L. Pulsipher

Publications and source records attributed to Joshua L. Pulsipher.

16 recordsLinked to original sources

arXiv2026

Solution Methods for Infinite-Dimensional Generalized Disjunctive Programming

Generalized disjunctive programming (GDP) expresses mixed discrete-continuous decisions through Boolean indicators and disjunctions, and can be systematically solved via a library of methods proposed in the literature. The recent InfiniteGDP abstraction lifts this modeling layer to continuous domains such as time, space, and uncertainty, but only the big-M and hull reformulations, the two endpoints of the relaxation spectrum, have been generalized to the infinite setting. This work closes this gap by generalizing four other GDP solution methods to infinite-dimensional optimization: the multiple big-M reformulation, P-split reformulation, cutting plane reformulation, and the logic-based outer approximation algorithm. It further proposes MBM-GP, a novel Gaussian-process variant of multiple big-M that learns the big-M function over the infinite domain from a small subset of the subproblem solves. Moreover, these approaches are implemented in the Julia package InfiniteDisjunctiveProgramming.jl. The methods are benchmarked on case studies arising in dynamic and stochastic optimization. The results demonstrate how the generalized solution methods can outperform big-M and hull, with MBM-GP retaining the tightness of multiple big-M at a fraction of its reformulation cost.

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arXiv2026

PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection

While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.

cs.LG↗

arXiv2026

GPU-Accelerated Direct Transcription-Based Nonlinear Model Predictive Control

In this paper, we present a GPU-accelerated framework for nonlinear model predictive control (NMPC) based on direct transcription and second-order interior-point methods. Many real-world systems exhibit nonlinear dynamics that cannot be accurately captured by linear models, motivating the use of NMPC. However, NMPC requires the repeated real-time solution of optimal control problems (OCP), which become computationally demanding large-scale nonlinear programs (NLPs) after transcription. Although GPU acceleration has emerged as a promising approach for nonlinear optimization, existing GPU-based NMPC workflows reconstruct structurally identical OCPs at each solve. This introduces substantial overhead even though successive solves differ only through updated system measurements or reference trajectories. To address this limitation, we introduce a parametric interior-point formulation that exploits the fixed structure of transcribed OCPs, enabling reuse of structure-dependent computations (e.g., symbolic factorization in sparse Cholesky) across re-solves. We evaluate the proposed framework on distillation column and 2D heated plate benchmarks against state-of-the-art CPU and GPU configurations. The results show that the framework achieves over an order-of-magnitude speedup in total NMPC run times. These improvements are primarily driven by reduced per-iteration solve times, with GPU execution achieving up to a 94% reduction compared to the baseline. Overall, the results demonstrate the effectiveness of exploiting repeated problem structure in GPU-accelerated NMPC and highlight the potential of the proposed framework to expand the envelope of real-time NMPC applications.

eess.SY↗

arXiv2025

A Digital Twin Simulator of a Pastillation Process with Applications to Automatic Control based on Computer Vision

We present a digital-twin simulator for a pastillation process. The simulation framework produces realistic thermal image data of the process that is used to train computer vision-based soft sensors based on convolutional neural networks (CNNs); the soft sensors produce output signals for temperature and product flow rate that enable real-time monitoring and feedback control. Pastillation technologies are high-throughput devices that are used in a broad range of industries; these processes face operational challenges such as real-time identification of clog locations (faults) in the rotating shell and the automatic, real-time adjustment of conveyor belt speed and operating conditions to stabilize output. The proposed simulator is able to capture this behavior and generates realistic data that can be used to benchmark different algorithms for image processing and different control architectures. We present a case study to illustrate the capabilities; the study explores behavior over a range of equipment sizes, clog locations, and clog duration. A feedback controller (tuned using Bayesian optimization) is used to adjust the conveyor belt speed based on the CNN output signal to achieve the desired process outputs.

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arXiv2025

A Comparison of Strategies to Embed Physics-Informed Neural Networks in Nonlinear Model Predictive Control Formulations Solved via Direct Transcription

This study aims to benchmark candidate strategies for embedding neural network (NN) surrogates in nonlinear model predictive control (NMPC) formulations that are subject to systems described with partial differential equations and that are solved via direct transcription (i.e., simultaneous methods). This study focuses on the use of physics-informed NNs and physics-informed convolutional NNs as the internal (surrogate) models within the NMPC formulation. One strategy embeds NN models as explicit algebraic constraints, leveraging the automatic differentiation (AD) of an algebraic modelling language (AML) to evaluate the derivatives. Alternatively, the solver can be provided with derivatives computed external to the AML via the AD routines of the machine learning environment the NN is trained in. The three numerical experiments considered in this work reveal that replacing mechanistic models with NN surrogates may not always offer computational advantages when smooth activation functions are used in conjunction with a local nonlinear solver (e.g., Ipopt), even with highly nonlinear systems. Moreover, in this context, the external function evaluation of the NN surrogates often outperforms the embedding strategies that rely on explicit algebraic constraints, likely due to the difficulty in initializing the auxiliary variables and constraints introduced by explicit algebraic reformulations.

eess.SY↗

arXiv2025

Event Constrained Programming

In this paper, we present event constraints as a new modeling paradigm that generalizes joint chance constraints from stochastic optimization to (1) enforce a constraint on the probability of satisfying a set of constraints aggregated via application-specific logic (constituting an event) and (2) to be applied to general infinite-dimensional optimization (InfiniteOpt) problems (i.e., time, space, and/or uncertainty domains). This new constraint class offers significant modeling flexibility in posing InfiniteOpt constraints that are enforced over a certain portion of their domain (e.g., to a certain probability level), but can be challenging to reformulate/solve due to difficulties in representing arbitrary logical conditions and specifying a probabilistic measure on a collection of constraints. To address these challenges, we derive a generalized disjunctive programming (GDP) representation of event constrained optimization problems, which readily enables us to pose logical event conditions in a standard form and allows us to draw from a suite of GDP solution strategies that leverage the special structure of this problem class. We also extend several approximation techniques from the chance constraint literature to provide a means to reformulate certain event constraints without the use of binary variables. We illustrate these findings with case studies in stochastic optimal power flow, dynamic disease control, and optimal 2D diffusion.

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arXiv2024

Optimal Reactive Operation of General Topology Supply Chain and Manufacturing Networks under Disruptions

Supply and manufacturing networks in the chemical industry involve diverse processing steps across different locations, rendering their operation vulnerable to disruptions from unplanned events. Optimal responses should consider factors such as product allocation, delayed shipments, and price renegotiation , among other factors. In such context, we propose a multiperiod mixed-integer linear programming model that integrates production, scheduling, shipping, and order management to minimize the financial impact of such disruptions. The model accommodates arbitrary supply chain topologies and incorporates various disruption scenarios, offering adaptability to real-world complexities. A case study from the chemical industry demonstrates the scalability of the model under finer time discretization and explores the influence of disruption types and order management costs on optimal schedules. This approach provides a tractable, adaptable framework for developing responsive operational plans in supply chain and manufacturing networks under uncertainty.

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arXiv2022

Convolutional Neural Networks: Basic Concepts and Applications in Manufacturing

We discuss basic concepts of convolutional neural networks (CNNs) and outline uses in manufacturing. We begin by discussing how different types of data objects commonly encountered in manufacturing (e.g., time series, images, micrographs, videos, spectra, molecular structures) can be represented in a flexible manner using tensors and graphs. We then discuss how CNNs use convolution operations to extract informative features (e.g., geometric patterns and textures) from the such representations to predict emergent properties and phenomena and/or to identify anomalies. We also discuss how CNNs can exploit color as a key source of information, which enables the use of modern computer vision hardware (e.g., infrared, thermal, and hyperspectral cameras). We illustrate the concepts using diverse case studies arising in spectral analysis, molecule design, sensor design, image-based control, and multivariate process monitoring.

cs.CV↗

arXiv2022

SAFE-OCC: A Novelty Detection Framework for Convolutional Neural Network Sensors and its Application in Process Control

We present a novelty detection framework for Convolutional Neural Network (CNN) sensors that we call Sensor-Activated Feature Extraction One-Class Classification (SAFE-OCC). We show that this framework enables the safe use of computer vision sensors in process control architectures. Emergent control applications use CNN models to map visual data to a state signal that can be interpreted by the controller. Incorporating such sensors introduces a significant system operation vulnerability because CNN sensors can exhibit high prediction errors when exposed to novel (abnormal) visual data. Unfortunately, identifying such novelties in real-time is nontrivial. To address this issue, the SAFE-OCC framework leverages the convolutional blocks of the CNN to create an effective feature space to conduct novelty detection using a desired one-class classification technique. This approach engenders a feature space that directly corresponds to that used by the CNN sensor and avoids the need to derive an independent latent space. We demonstrate the effectiveness of SAFE-OCC via simulated control environments.

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arXiv2022

Random Field Optimization

We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.

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arXiv2021

New Measures for Shaping Trajectories in Dynamic Optimization

We propose a new class of measures for shaping time-dependent trajectories in dynamic optimization (DO). The proposed measures are analogous to risk measures used in stochastic optimization (SO) and are inspired by a recently-proposed unifying abstraction for infinite-dimensional optimization. Risk measures are summarizing statistics (e.g., average, variance, quantiles, worst-case values) that are used to shape the probability density of random objectives and constraints. We show that this extensive collection of measures can be applied in DO for computing and manipulating interesting features of time-dependent trajectories (e.g., excursion costs and quantiles). We also discuss how to implement these measures in the Julia modeling package InfiniteOpt.jl.

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arXiv2021

A Unifying Modeling Abstraction for Infinite-Dimensional Optimization

Infinite-dimensional optimization (InfiniteOpt) problems involve modeling components (variables, objectives, and constraints) that are functions defined over infinite-dimensional domains. Examples include continuous-time dynamic optimization (time is an infinite domain and components are a function of time), PDE optimization problems (space and time are infinite domains and components are a function of space-time), as well as stochastic and semi-infinite optimization (random space is an infinite domain and components are a function of such random space). InfiniteOpt problems also arise from combinations of these problem classes (e.g., stochastic PDE optimization). Given the infinite-dimensional nature of objectives and constraints, one often needs to define appropriate quantities (measures) to properly pose the problem. Moreover, InfiniteOpt problems often need to be transformed into a finite dimensional representation so that they can be solved numerically. In this work, we present a unifying abstraction that facilitates the modeling, analysis, and solution of InfiniteOpt problems. The proposed abstraction enables a general treatment of infinite-dimensional domains and provides a measure-centric paradigm to handle associated variables, objectives, and constraints. This abstraction allows us to transfer techniques across disciplines and with this identify new, interesting, and useful modeling paradigms (e.g., event constraints and risk measures defined over time domains). Our abstraction serves as the backbone of an intuitive Julia-based modeling package that we call InfiniteOpt.jl. We demonstrate the developments using diverse case studies arising in engineering.

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arXiv2021

Measuring and Optimizing System Reliability: A Stochastic Programming Approach

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges). Under this setting, reliability is defined as the probability of finding a path between sources and sink nodes under random component failures and we show that this measure can be computed by solving a stochastic mixed-integer program. The stochastic programming setting allows us to account for system constraints and general probability distributions to characterize failures and allows us to derive optimization formulations that identify designs of maximum reliability. We also propose a strategy to approximately solve these problems in a scalable manner by using purely continuous formulations.

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arXiv2021

A Mixed-Integer Conic Programming Formulation for Computing the Flexibility Index under Multivariate Gaussian Uncertainty

We present a methodology for computing the flexibility index when uncertainty is characterized using multivariate Gaussian random variables. Our approach computes the flexibility index by solving a mixed-integer conic program (MICP). This methodology directly characterizes ellipsoidal sets to capture correlations in contrast to previous methodologies that employ approximations. We also show that, under a Gaussian representation, the flexibility index can be used to obtain a lower bound for the so-called stochastic flexibility index (i.e., the probability of having feasible operation). Our results also show that the methodology can be generalized to capture different types of uncertainty sets.

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arXiv2021

A Computational Framework for Quantifying and Analyzing System Flexibility

We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures for computing well-centered nominal points, and a procedure for identifying and ranking flexibility-limiting constraints and critical parameter values. These capabilities allow us to analyze the flexibility of complex systems such as distribution networks.

math.OC↗

arXiv2021

A Scalable Stochastic Programming Approach for the Design of Flexible Systems

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with a given target probability level. Unfortunately, joint chance constraints are complicated mathematical objects that often need to be reformulated using mixed-integer programming (MIP) techniques. In this work, we cast the design problem as a conflict resolution problem that seeks to minimize cost while maximizing flexibility. We propose a purely continuous relaxation of this problem that provides a significantly more scalable approach relative to MIP methods and show that the formulation delivers solutions that closely approximate the Pareto set of the original joint chance-constrained problem.

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