Silicon-on-insulator (SOI) thin layers offer a variety of mechanisms leading to high reconfigurable non-linear expressivity [1, 2], a functionality required for the physical implementation of novel networks, such as Kolmogorow-Arnold networks, and brain inspired computation. Physical neural networks (PNNs) traditionally aim to emulate the architecture of Multilayer Perceptrons (MLPs), where training is confined to linear weights and hardware nonlinearities are treated as fixed constraints. We recently reported on a paradigm shift by implementing Physical Kolmogorov-Arnold Networks (KANs) on Silicon-on-Insulator (SOI) technology [F. Taglietti, A. Pulici, M. Roxburgh, G. Seguini, I. Vidamour, S. Menzel, E. Franco, M. Laus, Eleni Vasilaki, M. Perego, T. J. Hayward, M. Fanciulli, J. C. Gartside, “Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks” https://arxiv.org/abs/2601.15340]. Unlike MLPs, KANs place learnable nonlinear functions directly on the edges of the network. We experimentally demonstrated this with Synaptic Nonlinear Elements (SYNEs), novel microscale SOI devices that exhibit highly reconfigurable nonlinear I-V characteristics. The intricate physics, rooted in non-equilibrium carrier transport and complex electrostatic interactions within the multi-gate SOI structure, generate rich nonlinearities including negative differential resistance (NDR) and multi-stable states. Crucially, the SYNE's configuration is augmented by a floating back-gate effect, wherein charge trapping within the dielectric layer modulates the local potential, possibly enabling long-term plasticity and persistent storage of the learned "function shape" rather than just a linear weight. To support our understanding of the device operation, we have performed 3D simulations using Synopsys Sentaurus TCAD. In the model we have included the SOI layer, the buried oxide and a portion of the doped Si substrate. Interface states at the Si/SiO₂ interfaces, revealed by electrically detected magnetic resonance (EDMR), with a Gaussian energy distribution have been considered to model presence of P_b0 centers. The simulated device characteristics qualitatively reproduce the experimental data, revealing the critical role of the floating back gate and of the interface defects, exploited to achieve the required non-linear expressivity. By leveraging the inherent "nonlinear heterogeneity" of SOI devices, we have shown that the variability of physical substrates can be a computational asset rather than a limitation. Our physical KANs operate at room temperature with microampere currents and 2 MHz speeds, consuming approximately 750 fJ per nonlinear operation. We validate this architecture across diverse tasks: i.e., nonlinear binary classification tasks and the prediction of Li-ion battery dynamics from noisy sensor data. Our results demonstrate that Physical KANs outperform equivalently-parameterized software MLPs and require up to two orders of magnitude fewer devices than conventional linear weight-based physical networks. This work establishes learned physical nonlinearity as a hardware-native computational primitive for efficient, compact, and high-performance neuromorphic SOI systems. We construct KAN synapses by summing the outputs of multiple SYNE devices in parallel. This creates a highly expressive, learnable edge that replaces the standard "weight \times input" operation. The hardware achieved 99.0% accuracy on the Yin-Yang classification task. Notably, the Physical KAN reached target accuracy with 100x fewer physical parameters than a standard linear PNN. This research demonstrates that the future of SOI-based neuromorphic hardware lies in embracing and training natural nonlinear complexities. Physical KANs provide a mathematically grounded framework to exploit these complexities, leading to AI hardware that is significantly more resource-efficient than current digital or analog-linear counterparts. SYNEs offers also the possibility to realize novel brain inspired devices, and this aspect will be also discussed.