Projection-based model order reduction (MOR) for systems with many input/output (I/O) ports has been a long-standing challenge. While existing techniques offer partial solutions, reducing systems with millions of nodes and tens of thousands of ports remains extremely difficult. Such reductions, however, are important in many modern industrial applications, such as chip power modeling for 3DIC. In this work, we propose a new strategy to address this problem using multi-fidelity machine learning. The process begins with an aggressive port reduction process, followed by a conventional MOR method such as PRIMA. This results in a reduced-order model (ROM) with (much) fewer ports, offering a low-fidelity approximation of the original system. Next, the original full-scale system is simulated in the time domain using representative input waveforms to generate a limited amount of high-fidelity data. This data is used to train a compensation network that learns to bridge the gap between the low-fidelity model output and the true system behavior. To further enhance the efficiency of compensation network training, we devise a tensorized mapping technique that captures the correlations across ports and transient responses, allowing the network to learn more effectively from limited high-fidelity samples. Numerical experiments demonstrate that our approach can solve large-scale MOR problems in a highly cost-effective and scalable manner. It also exhibits a promising level of generalizability in handling input waveforms that differ from the training data.

Exponential integrator (EI) methods have been a promising alternative to backward differentiation formulas (BDF) for transient circuit simulation. However, application of EI to generic nonlinear circuits has achieved only limited success so far, due to numerical instability and difficulty in combining with Newton iterations. In this work, we propose a new nonlinear EI framework, EI-TR, with a novel implicit regularization scheme and a truncated rational (TR) approximation for the treatment of nonlinear functions. The former employs a smart eigenvalue modification to avoid the system partition in the SOTA EI-NK that may induce numerical instability in nonlinear system partitioning. The latter decouples the solutions of the linear and nonlinear systems and reduces the three-layer nested iteration in EI-NK to one single Newton loop similar to conventional BDF, thereby significantly enhancing the performance and robustness of EI for generic nonlinear circuits. Numerical results demonstrate that EI-TR reduces Newton iterations by 3× compared to EI-NK and achieves 6.5x larger time steps than traditional trapezoidal methods.

Existing Multi-fidelity Bayesian Optimization (MFBO) methods ignore the convergence behavior of the multi-fidelity surrogate as the fidelity increases, leading to inefficient exploration and suboptimal performance. We introduce CAMO (Convergence-Aware Multi-fidelity Optimization), a principled framework based on Linear Fidelity Differential Equations (LFiDEs) that explicitly encodes convergence of fidelity-indexed outputs and employs a closed-form nonstationary kernel. We rigorously prove the existence and pointwise/uniform convergence to the high fidelity surrogate under mild restrictions and provide new convergence results for general FiDEs using smooth, non-smooth and even non-convex Lyapunov functions, establishing a bridge between MFBO and the theory of subgradient flows in non-smooth optimisation theory. Combined with a fidelity-aware acquisition function, CAMO outperforms state-of-the-art MFBO methods on a majority of synthetic and real-world benchmarks, with up to a four-fold improvement in optimisation performance and a dramatic speed-up in convergence. CAMO offers a tractable and theoretically grounded approach to convergence-aware MFBO.

As 3D integrated circuits (ICs) have emerged as a promising direction in the semiconductor industry, thermal issues in 3D-ICs have become increasingly prominent. In this work, we develop a novel machine learning (ML) thermal analysis framework, namely Autoregressive Operator (ARO), to address the pressing need for rapid yet highly accurate thermal predictions during the chip design process. Unlike traditional ML-based methods that can only deal with scenarios of well-defined input-output domains, ARO learns the thermal diffusion operator such that it can generalize to any unseen circuits and map the power traces to the steady-state/transient thermal spatial-temporal distributions. To further reduce the computational demand of data preparation, we equip ARO with multi-fidelity fusion to exploit the advantage of computationally cheap low-fidelity simulations and expensive high-fidelity simulations and active learning to guide the preparation of training data. Our results show that, for the unseen testing cases, a well-trained ARO can produce accurate results with about 1000× speedup compared to MTA. Moreover, equipped with active learning, ARO achieves at least 25% data reduction compared to pseudo-random strategies.