Towards a Theory of Systems Engineering Processes: A Principal-Agent Model of a One-Shot, Shallow Process

Systems engineering processes coordinate the effort of different individuals to generate a product satisfying certain requirements. As the involved engineers are self-interested agents, the goals at different levels of the systems engineering hierarchy may deviate from the system-level goals which may cause budget and schedule overruns. Therefore, there is a need of a systems engineering theory that accounts for the human behavior in systems design. To this end, the objective of this paper is to develop and analyze a principal-agent model of a one-shot (single iteration), shallow (one level of hierarchy) systems engineering process. We assume that the systems engineer maximizes the expected utility of the system, while the subsystem engineers seek to maximize their expected utilities. Furthermore, the systems engineer is unable to monitor the effort of the subsystem engineer and may not have a complete information about their types or the complexity of the design task. However, the systems engineer can incentivize the subsystem engineers by proposing specific contracts. To obtain an optimal incentive, we pose and solve numerically a bi-level optimization problem. Through extensive simulations, we study the optimal incentives arising from different system-level value functions under various combinations of effort costs, problem-solving skills, and task complexities

Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification

Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems contain unknown elements, such as missing parameters, noisy data, or incomplete physical laws, this is widely approached as an uncertainty quantification problem. The common techniques to handle all the variables typically depend on the numerical scheme used to approximate the posterior, and it is desirable to have a method which is independent of any such discretization. Information field theory (IFT) provides the tools necessary to perform statistics over fields that are not necessarily Gaussian. We extend IFT to physics-informed IFT (PIFT) by encoding the functional priors with information about the physical laws which describe the field. The posteriors derived from this PIFT remain independent of any numerical scheme and can capture multiple modes, allowing for the solution of problems which are ill-posed. We demonstrate our approach through an analytical example involving the Klein-Gordon equation. We then develop a variant of stochastic gradient Langevin dynamics to draw samples from the joint posterior over the field and model parameters. We apply our method to numerical examples with various degrees of model-form error and to inverse problems involving nonlinear differential equations. As an addendum, the method is equipped with a metric which allows the posterior to automatically quantify model-form uncertainty. Because of this, our numerical experiments show that the method remains robust to even an incorrect representation of the physics given sufficient data. We numerically demonstrate that the method correctly identifies when the physics cannot be trusted, in which case it automatically treats learning the field as a regression problem.Comment: 32 pages, 8 figures. Published in Journal of Computational Physic

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems