Physics-constrained Neural ODE compact modeling of multi-terminal MoS2 memtransistors for LTspice neuromorphic circuit simulation

Abstract

Compact models are required to connect multi-terminal molybdenum disulfide (MoS₂) memtransistors with standard circuit simulators, but only a limited number of such models are available. In this work, a physics-constrained neural ordinary differential equation (Neural ODE) compact model was developed and implemented as an LTspice behavioral subcircuit, in which the internal switching dynamics were learned from a reduced-order teacher. A Biolek-type directional window was combined with the exact hard-zero expression \({n}_{\theta }\left(w,{V}_{DS}\right)-{n}_{\theta }\left(w,0\right)\), due to which the state rate becomes exactly zero at zero drain–source voltage. The mean in-range coefficient of determination obtained for five seeds was \({R}^{2}=0.999874\pm 0.000055\). For the selected model, the out-of-range \({R}^{2}\) values at \(\pm 9\) and \(\pm 11\) V were 0.8506 and 0.7586, respectively, as compared to 0.6511 and 0.3595 for the fitted linear Biolek model. The hysteresis-area error was 34.03% for the learned model, as compared to 40.23% for the fitted linear model, whereas the linear model showed smaller low-conductance-state and pulse-nonlinearity errors. The normalized comparison with published MoS₂ memtransistor data showed good agreement for potentiation (\({R}^{2}=0.9755\)), whereas the agreement for depression curvature was weak (\({R}^{2}=0.2738\)). The state and current \({R}^{2}\) values obtained from the exported LTspice data both exceeded 0.999999, i.e., agreement at numerical precision. The results show that the model can be used as a circuit-compatible emulator within the investigated conditions, but it is not a replacement for calibration with measured device data.