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math.NA2026
Drift-Free Conservative Dynamics from Quantized Interaction Rules
Park Junhu, Youngsoo Ha, Myungjoo Kang
Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissi…
math.NA2026
Continuum dynamics from quantised interaction rules
Park Junhu, Youngsoo Ha, Myungjoo Kang
Hyperbolic conservation laws are conventionally solved by evolving reconstructed floating-point fields, incurring both computational overhead and structural diffusion near disconti…
math.NA2024
Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws
Taeyoung Kim, Myungjoo Kang
Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods hav…