Learning Control Policies of Hodgkin-Huxley Neuronal Dynamics

We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic outcomes by tailoring the parameters of a DBS system, typically via electrical stimulation, in real time based on the patient's ongoing neuronal activity. We approximate the value function offline using a neural network to enable generating controls (stimuli) in real time via the feedback form. The neuronal activity is characterized by a nonlinear, stiff system of differential equations as dictated by the Hodgkin-Huxley model. Our training process leverages the relationship between Pontryagin's maximum principle and Hamilton-Jacobi-Bellman equations to update the value function estimates simultaneously. Our numerical experiments illustrate the accuracy of our approach for out-of-distribution samples and the robustness to moderate shocks and disturbances in the system.

A SWAT-based Reinforcement Learning Framework for Crop Management

Crop management involves a series of critical, interdependent decisions or actions in a complex and highly uncertain environment, which exhibit distinct spatial and temporal variations. Managing resource inputs such as fertilizer and irrigation in the face of climate change, dwindling supply, and soaring prices is nothing short of a Herculean task. The ability of machine learning to efficiently interrogate complex, nonlinear, and high-dimensional datasets can revolutionize decision-making in agriculture. In this paper, we introduce a reinforcement learning (RL) environment that leverages the dynamics in the Soil and Water Assessment Tool (SWAT) and enables management practices to be assessed and evaluated on a watershed level. This drastically saves time and resources that would have been otherwise deployed during a full-growing season. We consider crop management as an optimization problem where the objective is to produce higher crop yield while minimizing the use of external farming inputs (specifically, fertilizer and irrigation amounts). The problem is naturally subject to environmental factors such as precipitation, solar radiation, temperature, and soil water content. We demonstrate the utility of our framework by developing and benchmarking various decision-making agents following management strategies informed by standard farming practices and state-of-the-art RL algorithms.

Forecasting Soil Moisture Using Domain Inspired Temporal Graph Convolution Neural Networks To Guide Sustainable Crop Management

Climate change, population growth, and water scarcity present unprecedented challenges for agriculture. This project aims to forecast soil moisture using domain knowledge and machine learning for crop management decisions that enable sustainable farming. Traditional methods for predicting hydrological response features require significant computational time and expertise. Recent work has implemented machine learning models as a tool for forecasting hydrological response features, but these models neglect a crucial component of traditional hydrological modeling that spatially close units can have vastly different hydrological responses. In traditional hydrological modeling, units with similar hydrological properties are grouped together and share model parameters regardless of their spatial proximity. Inspired by this domain knowledge, we have constructed a novel domain-inspired temporal graph convolution neural network. Our approach involves clustering units based on time-varying hydrological properties, constructing graph topologies for each cluster, and forecasting soil moisture using graph convolutions and a gated recurrent neural network. We have trained, validated, and tested our method on field-scale time series data consisting of approximately 99,000 hydrological response units spanning 40 years in a case study in northeastern United States. Comparison with existing models illustrates the effectiveness of using domain-inspired clustering with time series graph neural networks. The framework is being deployed as part of a pro bono social impact program. The trained models are being deployed on small-holding farms in central Texas.