Physics-Informed Machine Learning Meets the Extreme Benchmark Suite Challenge of the CATS Nuclear Reactor Point Kinetics Equations

High-fidelity numerical solutions of the point kinetics equations (PKEs) underpin nuclear reactor safety analyses, control system designs, and facility simulations. Despite decades of progress, most available solvers are validated against a narrow set of test cases and rarely exceed six to eight significant places, leaving an open question: Can a fundamentally different algorithmic paradigm, rooted in machine learning rather than classical discretization, achieve the extreme accuracy required for benchmark-quality verification?We address this question by applying the extreme theory of functional connections (X-TFC), a physics-informed machine learning framework, to the complete 35-case PKE extreme benchmark suite recently published by Ganapol, the most comprehensive and accurate reference suite currently available.The benchmark suite spans 17 distinct reactivity insertion types—step, ramp, sinusoidal, zig-zag, exponential, exponential sinusoidal, sinusoidal cosinusoidal, Gaussian, Bessel, damped sine, sine Gaussian exponential, Doppler feedback, Keepin compensated ramp, proportional feedback, internal factor Doppler, external factor Doppler, and convolution feedback—across six reactor parameterizations for one- and six-group delayed neutron models.Five algorithmic improvements over the original X-TFC PKE implementation—analytical Jacobian construction exploiting the PKE block structure, Lower-Upper (LU) factorization caching for constant coefficient cases, multiphase adaptive time grids, precomputed constant Jacobian blocks, and phase-dependent solver selection (LU versus QR)—enable X-TFC to reproduce the 12-place converged accelerated Taylor series (CATS) reference values to 12 significant places for all the prescribed reactivity cases and the state-dependent feedback cases, with solutions spanning up to 219 orders of magnitude.When embedded in arbitrary precision arithmetic, X-TFC reproduces the extreme 24-place Quadruple Precision CATS (QPCATS) step insertion benchmark to all 24 significant places. These results demonstrate that a physics-informed machine learning method can be validated against the gold-standard CATS/BEFD (Backward Euler Finite Difference) benchmarks to extreme precision, providing cross-paradigm confirmation from fundamentally different algorithmic perspectives and underscoring the indispensable role of trusted reference solutions in verifying new computational approaches.