arXiv subjects

Joel A. Paulson

Publications and source records attributed to Joel A. Paulson.

29 records · Page 2Linked to original sources

arXiv2024

Accelerating Black-Box Molecular Property Optimization by Adaptively Learning Sparse Subspaces

Molecular property optimization (MPO) problems are inherently challenging since they are formulated over discrete, unstructured spaces and the labeling process involves expensive simulations or experiments, which fundamentally limits the amount of available data. Bayesian optimization (BO) is a powerful and popular framework for efficient optimization of noisy, black-box objective functions (e.g., measured property values), thus is a potentially attractive framework for MPO. To apply BO to MPO problems, one must select a structured molecular representation that enables construction of a probabilistic surrogate model. Many molecular representations have been developed, however, they are all high-dimensional, which introduces important challenges in the BO process -- mainly because the curse of dimensionality makes it difficult to define and perform inference over a suitable class of surrogate models. This challenge has been recently addressed by learning a lower-dimensional encoding of a SMILE or graph representation of a molecule in an unsupervised manner and then performing BO in the encoded space. In this work, we show that such methods have a tendency to "get stuck," which we hypothesize occurs since the mapping from the encoded space to property values is not necessarily well-modeled by a Gaussian process. We argue for an alternative approach that combines numerical molecular descriptors with a sparse axis-aligned Gaussian process model, which is capable of rapidly identifying sparse subspaces that are most relevant to modeling the unknown property function. We demonstrate that our proposed method substantially outperforms existing MPO methods on a variety of benchmark and real-world problems. Specifically, we show that our method can routinely find near-optimal molecules out of a set of more than $>100$k alternatives within 100 or fewer expensive queries.

q-bio.BM↗

arXiv2023

No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations

This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which often arises in real-world science and engineering applications. We propose a novel method, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is a conceptually simple, deterministic approach that avoid constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable sample average approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation under a non-parametric Bayesian representation of the black-box function. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establis bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to most existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations when the original problem is infeasible (with high probability given the Bayesian model). Numerical experiments on several test problems, including environmental model calibration and real-time optimization of a reactor system, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees.

stat.ML↗

arXiv2023

Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

eess.SY↗

arXiv2023

Multi-agent Black-box Optimization using a Bayesian Approach to Alternating Direction Method of Multipliers

Bayesian optimization (BO) is a powerful black-box optimization framework that looks to efficiently learn the global optimum of an unknown system by systematically trading-off between exploration and exploitation. However, the use of BO as a tool for coordinated decision-making in multi-agent systems with unknown structure has not been widely studied. This paper investigates a black-box optimization problem over a multi-agent network coupled via shared variables or constraints, where each subproblem is formulated as a BO that uses only its local data. The proposed multi-agent BO (MABO) framework adds a penalty term to traditional BO acquisition functions to account for coupling between the subsystems without data sharing. We derive a suitable form for this penalty term using alternating directions method of multipliers (ADMM), which enables the local decision-making problems to be solved in parallel (and potentially asynchronously). The effectiveness of the proposed MABO method is demonstrated on an intelligent transport system for fuel efficient vehicle platooning.

math.OC↗

arXiv2022

Stochastic Physics-Informed Neural Ordinary Differential Equations

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic and nonlinear behavior. We propose a flexible and scalable framework for training artificial neural networks to learn constitutive equations that represent hidden physics within SDEs. The proposed stochastic physics-informed neural ordinary differential equation framework (SPINODE) propagates stochasticity through the known structure of the SDE (i.e., the known physics) to yield a set of deterministic ODEs that describe the time evolution of statistical moments of the stochastic states. SPINODE then uses ODE solvers to predict moment trajectories. SPINODE learns neural network representations of the hidden physics by matching the predicted moments to those estimated from data. Recent advances in automatic differentiation and mini-batch gradient descent with adjoint sensitivity are leveraged to establish the unknown parameters of the neural networks. We demonstrate SPINODE on three benchmark in-silico case studies and analyze the framework's numerical robustness and stability. SPINODE provides a promising new direction for systematically unraveling the hidden physics of multivariate stochastic dynamical systems with multiplicative noise.

cs.LG↗

arXiv2022

COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information

Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems.

math.OC↗

arXiv2020

A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization

The closed-loop performance of model predictive controllers (MPCs) is sensitive to the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization (BO) to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor example.

eess.SY↗

arXiv2020

Data-Driven Scenario Optimization for Automated Controller Tuning with Probabilistic Performance Guarantees

Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of blackbox optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This paper focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.

eess.SY↗

arXiv2015

Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states. A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.

math.OC↗

arXiv2015

Lyapunov-based Stochastic Nonlinear Model Predictive Control: Shaping the State Probability Density Functions

Stochastic uncertainties in complex dynamical systems lead to variability of system states, which can in turn degrade the closed-loop performance. This paper presents a stochastic model predictive control approach for a class of nonlinear systems with unbounded stochastic uncertainties. The control approach aims to shape probability density function of the stochastic states, while satisfying input and joint state chance constraints. Closed-loop stability is ensured by designing a stability constraint in terms of a stochastic control Lyapunov function, which explicitly characterizes stability in a probabilistic sense. The Fokker-Planck equation is used for describing the dynamic evolution of the states' probability density functions. Complete characterization of probability density functions using the Fokker-Planck equation allows for shaping the states' density functions as well as direct computation of joint state chance constraints. The closed-loop performance of the stochastic control approach is demonstrated using a continuous stirred-tank reactor.

math.OC↗

arXiv2015

Stability for Receding-horizon Stochastic Model Predictive Control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.

eess.SY↗