Efficiently solving DC operating points for large-scale nonlinear circuits in SPICE simulation is both critical and challenging. Pseudo transient analysis (PTA) is a widely used and promising approach for DC analysis, with the pseudo element embedding strategy playing a key role in ensuring convergence and simulation efficiency. In this paper, we present GPTA, a graph neural network (GNN) enhanced PTA method that adaptively positions embeddings by considering circuit topology. GPTA transforms the nonlinear DC circuits into linearized graph representations and then integrates multi-head messaging, adaptive message filtering, and multi-scale information fusion in the GNN model to improve feature extraction. Additionally, a layer-by-layer pooling and prediction strategy effectively retains intermediate layer information, enhancing model expressiveness. Numerical results show that GPTA significantly improves the efficiency of DC analysis in terms of both convergence and simulation speed.

Adjoint sensitivity analysis is critical in modern integrated circuit design and verification, but its computational intensity grows significantly with the circuit size, the number of objective functions, and the accumulation of time points. This growth can impede its wider application. The intimate link between the forward integration in transient analysis and the reverse integration in adjoint sensitivity analysis allows for the retention of Jacobian matrices from transient analysis, thereby speeding up sensitivity analysis. However, Jacobian matrices across multiple timesteps are often so large that they cannot be stored in memory during the forward integration process, necessitating disk storage and incurring significant I/O overhead. To address this, we develop a memory-efficient sensitivity analysis method that utilizes data compression to minimize memory overhead during simulation and enhance analysis efficiency. Our compression method can efficiently compress the sparse tensor that contains the Jacobian matrices over time by exploiting the spatiotemporal characteristics of the data and circuit attributes. It also introduces a shared-indices technique, a cutting-edge spatiotemporal prediction model, and robust residual encoding. We evaluate our compression method on 7 datasets from real-world simulations and demonstrate that it can reduce memory requirements by more than 16x on average, which is significantly more efficient than other state-of-the-art compression techniques.