David Grimsman

Changing wildfire regimes in recent decades have prompted extensive investigation into their hydrological impact. However, contradictory findings on post-fire flow regime changes have highlighted the complexity of this relationship. This study considers rich daily-resolution hydrological data on 898 burned catchments and over 8000 unburned control catchments to choose a set of 39 paired catchment experiments, along with 500 control pair experiments. We use these 500 control catchments to evaluate the extent to which the paired watershed approach accounts for hidden co-varying factors, finding that in most instances, it does not. We assess the influence of wildfires on flow magnitude, timing, and dynamicity. We also explore the effects of wildfire on water storage, evapotranspiration, and flood flows across the Western USA from 1984 to 2023. We find that percent changes in flow magnitude post-fire are not statistically significant and are uncorrelated with the percent of the catchment that burned, even when data are restricted to the critical first 5 years post-fire. However, linear regression analysis of 94 catchment variables found weak positive relationships between pre-fire forest cover and percent changes in flow magnitudes. Our results emphasize that the statistical uncertainty associated with even well-established methods may overshadow the magnitude of observed effects.

Deriving competitive, distributed solutions to multi-agent problems is cruncial for many developing application domains; Game theory has emerged as a useful framework to design such algorithms. However, much of the attention within this framework is on the study of equilibrium behavior, whereas transient behavior is often ignored. Therefore, in this paper we study the transient efficiency guarantees of best response processes in the context of submodular resource allocation games, which find application in various engineering contexts. Specifically, the main focus of this paper is on characterizing the optimal short-term system-level behavior under the best-response process. Interestingly, the resulting transient performance guarantees are relatively close to the optimal asymptotic performance guarantees. Furthermore, we characterize the trade-offs that result when optimizing for both asymptotic and transient efficiency through various utility designs.

Designing fast, distributed algorithms for multi-agent problems is vital for many novel application domains. Greedy algorithms have been shown in many multi-agent contexts to be an efficient approach to arrive at good solutions quickly. In this work, we ask the following: Is there any way to improve the performance of greedy algorithms without sacrificing the linear run-time guarantees? For this, we take inspiration from incentive design in the game-theoretic literature. In this work, we consider a modified version of the greedy algorithm where agents do not optimize against the global objective. Instead, each agent is prescribed an auxiliary utility function (which may differ from the original objective function) in which it optimizes under. By designing the utility functions properly, we show in this work that the resulting performance guarantees of the greedy algorithm can increase significantly. We study this approach in the context of resource-allocation games, which are used to model a rich variety of engineering applications. Interestingly, the performance guarantees from the modified greedy algorithm can be significantly close to the best centralized performance guarantees. The main technical contribution of the paper is the characterization of the performance guarantees through a linear program construction.

To navigate the evolving terrain of Supply Chains (SC), firms require new tools with broader applicability. Current research ignores the forest in favor of trees, with focal firms and serial networks assumed. This paper explicates a novel and scalable model for SC study at a broad level. We utilize the core of the model to observe the effect of structure and policy on demand disturbance in a SC as a whole. We find that complex structure alone does not effect change in disturbances; dynamic policy is necessary and sufficient for amplification. The model and simulations build to our main result: diversifying a firm's supplier-base can amplify disturbances more quickly.

We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to minimize estimation error. We select as a metric the Fisher Information Matrix (FIM), as "minimizing" the inverse of the FIM is required to achieve small estimation error. We propose to generate the optimal path from the Hamilton-Jacobi (HJ) partial differential equation (PDE) as it is the necessary and sufficient condition for optimality. A traditional method of lines (MOL) approach, based on a spatial grid, lends itself well to the highly non-linear and non-convex structure of the problem induced by the FIM matrix. However, the sensor placement problem results in a state space dimension that renders a naive MOL approach intractable. We present a new hybrid approach, whereby we decompose the state space into two parts: a smaller subspace that still uses a grid and takes advantage of the robustness to non-linearities and non-convexities, and the remaining state space that can by found efficiently from a system of ODEs, avoiding formation of a spatial grid.

This paper considers a set of sensors, which as a group are tasked with taking measurements of the environment and sending a small subset of the measurements to a centralized data fusion center, where the measurements will be used to estimate the overall state of the environment. The sensors’ goal is to send the most informative set of measurements so that the estimate is as accurate as possible. This problem is formulated as a submodular maximization problem, for which there exists a well-studied greedy algorithm, where each sensor sequentially chooses a set of measurements from its own local set, and communicates its decision to the future sensors in the sequence. In this work, sensors can additionally share measurements with one another, in order to augment the decision set of each sensor. We explore how this increase in communication can be exploited to improve the results of the nominal greedy algorithm. Specifically, we show that this measurement passing can improve the quality of the resulting measurement set by up to a factor of n + 1, where n is the number of sensors.

We show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time Invariant (LTI) systems by employing the Model Boundary Approximation Method (MBAM), a recent development in the Physics literature. We also show that MBAM provides a novel way to interpolate between Balanced Truncation and Balanced Singular Perturbation Approximation, by exploring the set of approximations on the boundary of the ``model manifold,'' which is associated with the specific choice of model parameterization and initial condition and is embedded in a sample space of measured outputs, between the elements that correspond to the two model reduction techniques. This work suggests similar types of approximations may be obtainable in topologically similar places (i.e. on certain boundaries) on the associated model manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted model reduction techniques to nonlinear systems.

We show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time Invariant (LTI) systems by employing the Model Boundary Approximation Method (MBAM), a recent development in the Physics literature. This unifying framework of these popular model reduction techniques shows that Balanced Truncation and Balanced Singular Perturbation Approximation each correspond to a particular boundary point on a manifold, the "model manifold," which is associated with the specific choice of model parameterization and initial condition, and is embedded in a sample space of measured outputs, which can be chosen arbitrarily, provided that the number of samples exceeds the number of parameters. We also show that MBAM provides a novel way to interpolate between Balanced Truncation and Balanced Singular Perturbation Approximation, by exploring the set of approximations on the boundary of the manifold between the elements that correspond to the two model reduction techniques; this allows for alternative approximations of a given system to be found that may be better under certain conditions. The work herein suggests similar types of approximations may be obtainable in topologically similar places (i.e. on certain boundaries) on the model manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted model reduction techniques to nonlinear systems.

Submodular maximization is an important problem with many applications in engineering, computer science, economics and social sciences. Since the problem is NP-Hard, a greedy algorithm has been developed, which gives an approximation within 1/2 of the optimal solution. This algorithm can be distributed among agents, each making local decisions and sharing that decision with other agents. Recent work has explored how the performance of the distributed algorithm is affected by a degradation in this information sharing. This work introduces the idea of strategy in these networks of agents and shows the value of such an approach in terms of the performance guarantees that it provides. In addition, an optimal strategy that gives such guarantees is identified.