KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation

TL;DR

KHRONOS is a novel kernel-based neural framework that achieves rapid, resource-efficient solutions for high-dimensional scientific problems, significantly outperforming traditional methods in accuracy and speed.

Contribution

It introduces a hierarchical kernel expansion approach for neural surrogates, enabling scalable, accurate, and fast solutions for complex PDEs and inverse problems.

Findings

Achieves over 100-fold error reduction compared to Kolmogorov Arnold Networks.

Provides sub-millisecond full-field predictions at arbitrary resolution.

Enables rapid inverse problem solving with sub-microsecond latency.

Abstract

Contemporary models of high dimensional physical systems are constrained by the curse of dimensionality and a reliance on dense data. We introduce KHRONOS (Kernel Expansion Hierarchy for Reduced Order, Neural Optimized Surrogates), an AI framework for model based, model free and model inversion tasks. KHRONOS constructs continuously differentiable target fields with a hierarchical composition of per-dimension kernel expansions, which are tensorized into modes and then superposed. We evaluate KHRONOS on a canonical 2D, Poisson equation benchmark: across 16 to 512 degrees of freedom (DoFs), it obtained L_2-square errors of 5e-4 down to 6e-11. This represents a greater than 100-fold gain over Kolmogorov Arnold Networks (which itself reports a 100 times improvement on MLPs/PINNs with 100 times fewer parameters) when controlling for the number of parameters. This also represents a 1e6-fold improvement in L_2-square error compared to standard linear FEM at comparable DoFs. Inference complexity is dominated by inner products, yielding sub-millisecond full-field predictions that scale to an arbitrary resolution. For inverse problems, KHRONOS facilitates rapid, iterative level set recovery in only a few forward evaluations, with sub-microsecond per sample latency. KHRONOS's scalability, expressivity, and interpretability open new avenues in constrained edge computing, online control, computer vision, and beyond.