Emerging Kolmogorov–Arnold networks (KANs) replace the linear weights of neural networks with trainable nonlinear functions. This modification is particularly attractive for scientific computing, where KANs can match the accuracy of conventional multilayer perceptrons (MLPs) while reducing model size by up to 100×. However, this efficiency comes at the cost of computationally expensive nonlinear evaluations, unlike conventional MLPs dominated by linear matrix multiplications. We present a flexible and energy-efficient compute-in-memory accelerator tailored for KANs, developed through cross-layer optimization across algorithm, architecture, circuit, and device levels. The accelerator computes arbitrary nonlinear functions using a single-read scheme and read-optimized memory arrays with nonvolatile memristive devices. Our system achieves a lowest energy of 8.69 pJ per KAN function. In terms of energy-delay product, it provides 1996× improvement over CPUs, 208× over standard MLP-oriented compute-in-memory accelerators, and up to 71× over prior KAN accelerators. These results establish energy-efficient hardware primitives for implementing advanced nonlinear networks in scientific computing.