Stefano Grivet-Talocia’s research while affiliated with Polytechnic University of Turin and other places

We introduce a framework for data-driven model order reduction of parameterized LTI systems with guaranteed uniform dissipativity. The strategy casts the problem into a multivariate rational fitting scheme that formally preserves the bounded realness of the model response. The formulation relies on the solution of a semi-definite program arising from a rational parameterization based on Bernstein polynomials. The models can be employed in system-level simulations both in the frequency and time domain.

This application paper addresses the problem of transient simulation of system-level Power Distribution Networks (PDN) of multicore processing systems. In particular, we consider a post-layout Power Integrity verification problem where all system parts are finalized and a highly accurate transient verification is performed to ensure that voltage supply signals remain within prescribed bounds when the PDN is loaded by realistic current stimuli. Systems with tens of even hundreds of cores are considered, equipped with per-core local voltage stabilization, attained through Integrated Voltage Regulators (IVR) suitably controlled by sensing and feedback loops. Transient simulation of such system-level PDNs becomes particularly challenging when interconnect models or macromodels computed by electromagnetic solvers are embedded. In order to break system complexity, we propose a set of algorithms based on an ad-hoc system partitioning strategy, combined with multi-level Waveform Relaxation (WR) schemes. The main advantage of this approach is a straightforward parallelization, aimed at solving concurrently by parallel computing threads only small and well-defined circuit partitions. Several partitioning and associated WR schemes are discussed and tested, showing excellent scalability with up to 60 computing threads, with significant speedup in runtime with respect to a standard SPICE-based approach.

This paper proposes a comprehensive model order reduction framework to enable fast power integrity verification at the system level. This approach is developed to compress models of complete power delivery networks of high-end multiprocessor systems, where electromagnetic models of board and package are connected through banks of per-core Fully Integrated Voltage Regulators to chip models and loads in a closed-loop configuration. Due to complexity in both dynamical behavior and number of signals to be monitored, a direct transient simulation at the system level is very challenging. We show that a careful topological formulation of the circuit equations leads to a global model format that enables a structured projection framework for the elimination of the redundant states. Within this framework, we present and compare two alternative approaches based on approximate interpolation and empirical balancing. In both cases, the resulting system is proven to be unconditionally stable both in open and in closed-loop configuration. Transient simulation of the reduced system provides a speedup exceeding 100× with respect to SPICE.

The 28th IEEE Workshop on Signal and Power Integrity (SPI 2024) was held from May 12 to 15, 2024, in Lisbon, Portugal. The IEEE EMC Society was a Technical Co-Sponsor of the event. Bringing together 87 participants from 19 countries spread throughout three continents, the SPI 2024 technical program included 24 oral and 11 poster presentations, for a total of 35 papers presented and now published in the IEEE Xplore® Digital Library.

Common design and verification flows of electronic systems under Signal and/or Power Integrity (SI/PI) constraints often rely on the availability of accurate macromodels of components and interconnects. Such macromodels enable fast transient analysis at the system level and consequently the possibility to efficiently verify the quality of the design. Several approaches are available to construct macromodels whose response accurately matches the raw data used for their identification, most often tabulated scattering responses. However, for the sake of SI/PI optimization, it is mandatory that such models reproduce accurately the underlying structure response when inserted as a component in a larger network, possibly subjected to different or uncertain port termination schemes. This capability is not inherently guaranteed by standard macromodeling approaches. Recently, the authors proposed a modified Vector Fitting (VF) iteration that overcomes this issue, by optimizing the macromodel accuracy with respect to sets of arbitrary terminations. This work completes this robust macromodeling framework by introducing a companion perturbation-based passivity enforcement scheme that preserves the macromodel accuracy with respect to the prescribed set of loads. The main innovation is the definition of a novel loss function to drive the perturbation routine, that allows to correct the non-passive model while preserving the required robust performance. Numerical evidence on a set of relevant Power Delivery Network (PDN) benchmarks confirms the effectiveness of the proposed approach.

In recent years, the Adaptive Antoulas-Anderson (AAA) algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI) systems represents one of the many applications in which this algorithm has proven to be successful since it typically generates reduced-order models (ROMs) efficiently and in an automated way. Despite its effectiveness and numerical reliability, the classical AAA algorithm is not guaranteed to return a ROM that retains the same structural features of the underlying dynamical system, such as the stability of the dynamics. In this paper, we propose a novel algebraic characterization for the stability of ROMs with transfer function obeying the AAA barycentric structure. We use this characterization to formulate a set of convex constraints on the free coefficients of the AAA model that, whenever verified, guarantee by construction the asymptotic stability of the resulting ROM. We suggest how to embed such constraints within the AAA optimization routine, and we validate experimentally the effectiveness of the resulting algorithm, named stabAAA, over a set of relevant MOR applications.