Accelerating Global optimisation with Piecewise-Linear Kolmogorov-Arnold Network Surrogates

Neural surrogates can provide highly accurate approximations of complex functions, yet this alone does not guarantee reliable and efficient downstream global optimisation. When neural networks are embedded into mathematical programs, their architecture and representation directly affect formulation size, relaxation strength, and ultimately the optimisation runtime. This paper focuses on continuous piecewise-linear Kolmogorov–Arnold networks (CPWL-KAN), whose learnable edge functions are parametrised as linear combinations of ReLU functions and admit exact mixed-integer programming (MIP) representations. Three CPWL-KAN variants are considered, which correspond to different weight combinations and expressivity properties. Numerical experiments conducted across three benchmark functions and an engineering optimisation problem show that CPWL-KANs can provide predictive accuracy comparable to, and sometimes better than, that of conventional ReLU MLPs of similar complexity; but the computational runtime with MIP solvers to certify global optimality of the surrogates can be significantly lower with CPWL-KANs embedded. Overall, these results demonstrate that functional parametrisation of neural surrogates is as important as predictive accuracy when their intended use is in downstream optimisation.