Data-driven discovery of the governing equations of dynamical systems via moving horizon optimization.

Discovering the governing laws underpinning physical and chemical phenomena entirely from data is a key step towards understanding and ultimately controlling systems in science and engineering. Noisy measurements and complex, highly nonlinear underlying dynamics hinder the identification of such governing laws. In this work, we introduce a machine learning framework rooted in moving horizon nonlinear optimization for identifying governing equations in the form of ordinary differential equations from noisy experimental data sets. Our approach evaluates sequential subsets of measurement data, and exploits statistical arguments to learn truly parsimonious governing equations from a large dictionary of basis functions. The proposed framework reduces gradient approximation errors by implicitly embedding an advanced numerical discretization scheme, which improves robustness to noise as well as to model stiffness. Canonical nonlinear dynamical system examples are used to demonstrate that our approach can accurately recover parsimonious governing laws under increasing levels of measurement noise, and outperform state of the art frameworks in the literature. Further, we consider a non-isothermal chemical reactor example to demonstrate that the proposed framework can cope with basis functions that have nonlinear (unknown) parameterizations.

Modeling, state estimation, and optimal control for the US COVID-19 outbreak.

The novel coronavirus SARS-CoV-2 and resulting COVID-19 disease have had an unprecedented spread and continue to cause an increasing number of fatalities worldwide. While vaccines are still under development, social distancing, extensive testing, and quarantining of confirmed infected subjects remain the most effective measures to contain the pandemic. These measures carry a significant socioeconomic cost. In this work, we introduce a novel optimization-based decision-making framework for managing the COVID-19 outbreak in the US. This includes modeling the dynamics of affected populations, estimating the model parameters and hidden states from data, and an optimal control strategy for sequencing social distancing and testing events such that the number of infections is minimized. The analysis of our extensive computational efforts reveals that social distancing and quarantining are most effective when implemented early, with quarantining of confirmed infected subjects having a much higher impact. Further, we find that "on-off" policies alternating between strict social distancing and relaxing such restrictions can be effective at "flattening" the curve while likely minimizing social and economic cost.

Process Control and Energy Efficiency.

We review the impact of control systems and strategies on the energy efficiency of chemical processes. We show that, in many ways, good control performance is a necessary but not sufficient condition for energy efficiency. The direct effect of process control on energy efficiency is manyfold: Reducing output variability allows for operating chemical plants closer to their limits, where the energy/economic optima typically lie. Further, good control enables novel, transient operating strategies, such as conversion smoothing and demand response. Indirectly, control systems are key to the implementation and operation of more energy-efficient plant designs, as dictated by the process integration and intensification paradigms. These conclusions are supported with references to numerous examples from the literature.

Full Closed-Loop Tests for the Relay Feedback Autotuning of Stable, Integrating, and Unstable Processes.

The relay (on-off) controller can stabilize wide ranges of processes including open-loop stable, integrating, and unstable processes, producing sustained oscillations. For improved proportional-integral-derivative controller tunings, methods to find process models with mixed closed-loop tests of relay feedback and proportional-derivative (PD) controllers are proposed. For unknown processes with arbitrary initial states, relay feedback tests are first applied and, after cyclic steady states are obtained, PD controllers or other relay feedback tests with set point changes are followed. This full closed-loop operation is desirable for integrating and unstable processes and will be useful even for stable processes when processes are far from their desirable operating points. Refined methods to find exact frequency responses of processes from initial and final cyclic steady states are derived. Whole relay feedback responses need not be saved. Several integrals at the relay switching times are used without iterative tests or computations.

Integrative FourD omics approach profiles the target network of the carbon storage regulatory system.

Multi-target regulators represent a largely untapped area for metabolic engineering and anti-bacterial development. These regulators are complex to characterize because they often act at multiple levels, affecting proteins, transcripts and metabolites. Therefore, single omics experiments cannot profile their underlying targets and mechanisms. In this work, we used an Integrative FourD omics approach (INFO) that consists of collecting and analyzing systems data throughout multiple time points, using multiple genetic backgrounds, and multiple omics approaches (transcriptomics, proteomics and high throughput sequencing crosslinking immunoprecipitation) to evaluate simultaneous changes in gene expression after imposing an environmental stress that accentuates the regulatory features of a network. Using this approach, we profiled the targets and potential regulatory mechanisms of a global regulatory system, the well-studied carbon storage regulatory (Csr) system of Escherichia coli, which is widespread among bacteria. Using 126 sets of proteomics and transcriptomics data, we identified 136 potential direct CsrA targets, including 50 novel ones, categorized their behaviors into distinct regulatory patterns, and performed in vivo fluorescence-based follow up experiments. The results of this work validate 17 novel mRNAs as authentic direct CsrA targets and demonstrate a generalizable strategy to integrate multiple lines of omics data to identify a core pool of regulator targets.

Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.

Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.

Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature.

We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic, convex-repulsive pair potentials that maximize the density range for which a two-dimensional square lattice is the stable ground state subject to a constraint on the chemical potential advantage it exhibits over competing structures (i.e., "depth" of the associated minimum on the chemical potential hypersurface). We formulate the design problem as a nonlinear program, which we solve numerically. This allows us to efficiently find optimized interactions for a wide range of possible chemical potential constraints. We find that assemblies designed to exhibit a large chemical potential advantage at a specified density have a smaller overall range of densities for which they are stable. This trend can be understood by considering the separation-dependent features of the pair potential and its gradient required to enhance the stability of the target structure relative to competitors. Using molecular dynamics simulations, we further show that potentials designed with larger chemical potential advantages exhibit higher melting temperatures.

Optimizing metabolite production using periodic oscillations.

Methods for improving microbial strains for metabolite production remain the subject of constant research. Traditionally, metabolic tuning has been mostly limited to knockouts or overexpression of pathway genes and regulators. In this paper, we establish a new method to control metabolism by inducing optimally tuned time-oscillations in the levels of selected clusters of enzymes, as an alternative strategy to increase the production of a desired metabolite. Using an established kinetic model of the central carbon metabolism of Escherichia coli, we formulate this concept as a dynamic optimization problem over an extended, but finite time horizon. Total production of a metabolite of interest (in this case, phosphoenolpyruvate, PEP) is established as the objective function and time-varying concentrations of the cellular enzymes are used as decision variables. We observe that by varying, in an optimal fashion, levels of key enzymes in time, PEP production increases significantly compared to the unoptimized system. We demonstrate that oscillations can improve metabolic output in experimentally feasible synthetic circuits.