Physics-Informed Neural Operator Inversion Tools for Improved Density Functional Theory

A vital component to managing the energy crisis is the development of photovoltaics, technologies which are driven by electron behavior. These behaviors can be modeled with computational simulation methods, the most widely used method being density functional theory (DFT). Unfortunately, current implementations of time-dependent DFT used to simulate the excited states of light harnessing processes cannot fully describe the double excitations, charge transfer, or temperature effects common in these technologies, necessitating further development of ensemble and thermal variants of DFT. Careful approximation of the electron-electron interaction is central to these improvements. Inversions in Kohn-Sham (KS) DFT, which take a density and return the exchange-correlation potential, can be used as a method of analysis and improvement. Additionally, continued advancements in machine-learning techniques like the use of neural operators, function-to-function mappings on infinite-dimensional function spaces, are also opening new pathways to these approximations. This work has begun by constructing a library of ground-state molecular system training data for building the first real-space physics-informed neural operator (PINO)-based density-to-potential inverter. The PINO has been applied to model test systems of the one-dimensional heat equation and the one-dimensional hydrogen molecule, establishing familiarity with the machine-learning architecture and a hyperparameter optimization framework. Initial steps toward the ultimate goal of expanding the application of the PINO inversion method to more realistically complex systems are underway and will be discussed. Critically, our PINO density-to-potential inversions can be extended toward extracting exact temperature or ensemble weight dependencies, broadening our work to thermal and ensemble DFT.