Author

N. Mysore

View on Semantic Scholar

2 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

#machine learning Preprint Sep 2026

Recovering Governing Dynamics from Distributed Observations via Exact Spline Merging

Scientific observations are frequently distributed across locations, time periods, and institutions. Combining such observations into a continuous, differentiable field enables recovering governing physical parameters from its derivatives. This paper makes two contributions in this setting. First, the established additive structure of fixed-basis ridge-regression statistics is applied to tensor-product spline fields: each data holder computes a local Gram matrix and moment vector, and the merged solution is mathematically identical to centralized fitting, with no raw data shared and no iterative synchronization. This property is specific to the fixed-feature squared-error setting; the present derivation does not establish an analogous guarantee for general jointly trained multilayer networks. Second, a complete pipeline connects distributed observations to physical parameter inference through field reconstruction, derivative extraction, and linear regression. The pipeline is validated on four PDEs: diffusion, wave, heat-with-source, and the nonlinear viscous Burgers equation, recovering governing parameters to sub-percent accuracy in the linear cases and 5\% for Burgers. In all cases, distributed merging introduces zero degradation relative to centralized fitting. Application to 41 years of NOAA sea-surface temperature data confirms the result on real spatiotemporal observations. Source code to reproduce all experiments is available at https://github.com/NAVEENMN/gramfield.

N. Mysore · 0 citations

#machine learning Preprint Sep 2026

InKAN: B-Spline KANs via Truncated Power Form

Kolmogorov-Arnold Networks (KANs) place learnable B-spline activations on network edges rather than fixed activations on nodes. The standard Cox-de Boor recursion evaluates these activations through $k$ sequential passes for degree-$k$ splines, consuming over 90% of forward-pass time. InKAN replaces this recursion with the truncated power form, a classical result from approximation theory that expresses each uniform cubic B-spline as five $(x)_+^3$ terms at shifted knot positions. The resulting expression computes exact B-spline basis values: the same mathematical function as the Cox-de Boor recursion, evaluated without sequential passes. This paper documents three contributions: (1) an implementation structured for torch . compile fusion, eliminating recursion, span lookup, and scatter-gather operations; (2) a bounded-coordinate evaluation that clamps the normalized input to $[0, k{+}1]$, preventing the growth of cancellation error at large off-support coordinates; and (3) an open-source package (pip install inkan). In the tested configurations, InKAN has 2.8--3.5$\times$ lower forward-pass latency than the Cox-de Boor recursion. Partition-of-unity errors remain below $10^{-5}$ for grid sizes up to 200.

N. Mysore · 0 citations