William Farlessyost

William Farlessyost, Sebastian Oberst, Shweta Singh

This paper introduces a novel framework for optimizing observer-based soft sensors through dynamic causality analysis. Traditional approaches to sensor selection often rely on linearized observability indices or statistical correlations that fail to capture the temporal evolution of complex systems. We address this gap by leveraging liquid-time constant (LTC) networks, continuous-time neural architectures with input-dependent time constants, to systematically identify and prune sensor inputs with minimal causal influence on state estimation. Our methodology implements an iterative workflow: training an LTC observer on candidate inputs, quantifying each input's causal impact through controlled perturbation analysis, removing inputs with negligible effect, and retraining until performance degradation occurs. We demonstrate this approach on three mechanistic testbeds representing distinct physical domains: a harmonically forced spring-mass-damper system, a nonlinear continuous stirred-tank reactor, and a predator-prey model following the structure of the Lotka-Volterra model, but with seasonal forcing and added complexity. Results show that our causality-guided pruning consistently identifies minimal sensor sets that align with underlying physics while improving prediction accuracy. The framework automatically distinguishes essential physical measurements from noise and determines when derived interaction terms provide complementary versus redundant information. Beyond computational efficiency, this approach enhances interpretability by grounding sensor selection decisions in dynamic causal relationships rather than static correlations, offering significant benefits for soft sensing applications across process engineering, ecological monitoring, and agricultural domains.

William Farlessyost, Shweta Singh

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources respectively, thus playing an important role in assessing sustainability of these systems. However, current dynamic models for these systems exist as mechanistic models, simulation of which is computationally intensive and does not provide a simplified understanding of the mechanisms driving the overall dynamics. For such systems, lower-order models can prove useful to enable sustainability analysis through coupled dynamical analysis. There have been few attempts at finding low-order models of manufacturing and natural systems, with existing work focused on model development of individual mechanism level. This work seeks to fill this current gap in the literature of developing simplified dynamical models for these systems by developing reduced-order models using a machine learning (ML) approach. The approach is demonstrated on an entire soybean-oil to soybean-diesel process plant and a lake system. We use a grey-box ML method with a standard nonlinear optimization approach to identify relevant models of governing dynamics as ODEs using the data simulated from mechanistic models. Results show that the method identifies a high accuracy linear ODE models for the process plant, reflective of underlying linear stoichiometric mechanisms and mass balance driving the dynamics. For the natural systems, we modify the ML approach to include the effect of past dynamics, which gives non-linear ODE. While the modified approach provides a better match to dynamics of stream flow, it falls short of completely recreating the dynamics. We conclude that the proposed ML approach work well for systems where dynamics is smooth, such as in manufacturing plant whereas does not work perfectly well in case of chaotic dynamics such as water stream flow.