KHRONOS：一种基于核的神经架构，用于快速、资源高效的科学计算
KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation
AI总结：
KHRONOS是一种基于核展开的神经架构，通过逐维核层次组合构建连续场，在泊松方程基准上实现比KAN高100倍、比线性FEM高1e6倍的精度提升，支持快速推理和逆问题求解。
摘要：
当代高维物理系统的模型受到维度灾难和对密集数据的依赖的制约。我们引入了KHRONOS（核展开层次结构用于降阶、神经优化的替代模型），这是一个用于基于模型、无模型和模型反演任务的人工智能框架。KHRONOS通过逐维核展开的层次组合构建连续可微的目标场，这些展开被张量化成模态，然后叠加。我们在一个经典的二维泊松方程基准上评估了KHRONOS：在16到512个自由度（DoFs）范围内，它获得了从5e-4到6e-11的L2平方误差。这代表了在控制参数数量时，相较于Kolmogorov Arnold网络（其自身报告在参数少100倍的情况下，比MLPs/PINNs有100倍的改进）超过100倍的增益。这也代表了在可比DoFs下，相较于标准线性有限元方法，L2平方误差有1e6倍的改进。推理复杂度主要由内积主导，产生亚毫秒级的全场预测，可扩展到任意分辨率。对于逆问题，KHRONOS仅需几次前向评估即可实现快速、迭代的水平集恢复，每次样本延迟低于微秒。KHRONOS的可扩展性、表达性和可解释性为受限边缘计算、在线控制、计算机视觉等领域开辟了新途径。
英文摘要：
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.
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