# Research

The three pillars of the SEA-CROGS center research are neural operators, graph networks, and spiking neural networks, with three cross-cutting themes in mathematics of machine learning, uncertainty quantification and trustworthy physics-informed machine intelligence, and causal inference. These pillars allow co-design of mathematics and computing hardware to augment foundational understanding and optimal control of complex systems spanning extremely disparate scales, e.g., climate modeling processes, as well as embedded systems and systems-of-systems requiring causal inference and physics-informed modeling.

**Neural operators **(task lead: Panos Stinis) develops a plurality of neural operators that are mathematically rigorous and can be trained by multimodal/multifidelity data, have the ability to multitask and learn continually, are stable across diverse environments, can accelerate conventional solvers and existing legacy codes, and can significantly enhance accuracy in coarse-grid climate simulations.

**Graph Networks** (task lead: Nat Trask) develops multimodal graph kernel/neural networks with probabilistic underpinnings to support submodel coupling of systems-of-systems, uncertainty quantification, fingerprinting, and causal analysis, providing a rigorous mathematical framework for both studying climate processes spanning Energy Exascale Earth System Model (E3SM) subsystems and detecting rare events with embedded systems of smart sensors.

**Spiking Neural Networks **(task lead: Priya Panda) develops spiking networks and other novel power-efficient architectures that learn nonlinear multi-operators and can solve problems at a higher level of abstraction and 1,000 times faster, hence developing the next generation of neural operators such as spiking DeepONet for real-time forecasting of multiphysics systems.