Ike Griss Salas

Ike Griss Salas, Ethan King

Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide limited excitation and model discovery is often non-unique. We propose a minimally structured Neural Ordinary Differential Equation (NODE) architecture that enforces trajectory stability and provides a tractable parameterization for multistable systems, by learning a vector field in the form $F(x,u) = f(x)\,(x - g(x,u))$, where $f(x) < 0$ elementwise ensures contraction and $g(x,u)$ determines the multi-attractor locations. Across several nonlinear benchmarks, the proposed structure is efficient on short time horizon training, captures multiple basins of attraction, and enables efficient gradient-based feedback control through the implicit equilibrium map $g$.

Alexander W. Hsu, Ike Griss Salas, Jacob M. Stevens-Haas et al.

We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE. Our numerical experiments reveal that the proposed strategy leads to significant gains in terms of accuracy, sample efficiency, and robustness to noise, both in terms of learning the equation and estimating the unknown states. This work demonstrates capabilities well beyond existing and widely used algorithms while extending the modeling flexibility of other recent developments in equation discovery.

Ike Griss Salas, Megan R. Ebers, Jake Stevens-Haas et al.

Monitoring the atmospheric dispersion of pollutants is increasingly critical for environmental impact assessments. High-fidelity computational models are often employed to simulate plume dynamics, guiding decision-making and prioritizing resource deployment. However, such models can be prohibitively expensive to simulate, as they require resolving turbulent flows at fine spatial and temporal resolutions. Moreover, there are at least two distinct dynamical regimes of interest in the plume: (i) the initial ejection of the plume where turbulent mixing is generated by the shear-driven Kelvin-Helmholtz instability, and (ii) the ensuing turbulent diffusion and advection which is often modeled by the Gaussian plume model. We address the challenge of modeling the initial plume generation. Specifically, we propose a data-driven framework that identifies a reduced-order analytical model for plume dynamics -- directly from video data. We extract a time series of plume center and edge points from video snapshots and evaluate different regressions based to their extrapolation performance to generate a time series of coefficients that characterize the plume's overall direction and spread. We regress to a sinusoidal model inspired by the Kelvin-Helmholtz instability for the edge points in order to identify the plume's dispersion and vorticity. Overall, this reduced-order modeling framework provides a data-driven and lightweight approach to capture the dominant features of the initial nonlinear point-source plume dynamics, agnostic to plume type and starting only from video. The resulting model is a pre-cursor to standard models such as the Gaussian plume model and has the potential to enable rapid assessment and evaluation of critical environmental hazards, such as methane leaks, chemical spills, and pollutant dispersal from smokestacks.