Physics-Aware Quantum Neural Network Modeling of Earth Science Phenomena

The increasing number of extreme weather events has also fueled a desire for accurate, in-time prediction tools. An example of recent research success lies in data-driven models for short-to-mid-term weather forecasting, which have outperformed traditional numerical weather predictions in hundreds of test cases [1, 2]. These results have sparked interest in high-resolution modeling of large-scale, complex phenomena for use in digital twins, such as NVIDIA's Earth-2 project and NASA's current Earth System Digital Twin effort. The main driver behind this interest is the potential of learning based methods (e.g., [2]) in solving partial differential equations (PDEs), which form the foundation of many Earth Science focus areas. In comparison to traditional solvers, these are capable of solving problems with more complex geometries and can sample the solution at arbitrary precision. In realistic scenarios where the complex processes may not be completely understood, they have the potential for pattern discovery and predictions of phenomena given partial knowledge and have the advantage of using empirical data to inform their solutions. The learning based methods hold promise but can be hard to optimize and can scale poorly as the problem becomes increasingly complex [3, 4]. On the other hand, quantum computers offer a fundamentally different paradigm of computation and can solve certain classes of problems exponentially faster than their classical counterparts [5--8]. Recent results promise an advantage for certain specialized differential equations in the long term [9--13]. However, much remains unknown about the full potential of quantum algorithms for differential equations in general outside a few initial studies [14--18] with their own promise and roadblocks. The objective of this proposal is to develop physics aware quantum-classical hybrid neural networks to solve for complex partial differential equations describing multiple interconnected earth systems. We will assess our method on ocean dynamics studies by solving the shallow water, barotropic and baroclinic equations. We will first numerically and analytically analyze and compare the current state of art quantum and classical learning based approaches for solving PDEs. The current architectures can be difficult to train as they can be too expressive and are agnostic to the physical problem. They use physics-based terms only in the loss as a soft constraint which does not guarantee that the PDE is satisfied exactly. We will explore using PDEs to initialize the training parameters and in selecting the training architecture. We will also explore embedding the PDE in the learning ansatz for quantum compatible approaches. This will help alleviate the trainability problem of quantum learning methods and increase their effectiveness in solving complex coupled PDEs. This shall allow us to use quantum and quantum compatible approaches to obtain fast and accurate solutions to solve PDEs describing various Earth-Science systems. Finally we will present a report, publication and release software showcasing our findings. Our work will provide a proof of principle that quantum technology can be applied to predict complex earth science phenomena. As quantum technology advances, it will offer a roadmap for addressing much more complex problems on a large scale in the future. Applications of this technology will mostly be explored in the context of the fluid mechanics of ocean dynamics. Natural applications include coastal zone digital twins and the interface between ocean currents, land, and atmosphere. Further applications could integrate this technology with ocean carbon process analysis and intermediate- term weather forecasting. Our goal will be to develop our model and analysis in a way that can be interoperable with other Earth system models and extensible to other settings and governing equations.

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