Fabio Semperlotti

John P. Hollkamp, Mihir Sen, Fabio Semperlotti

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Siddharth Nair, Timothy F. Walsh, Greg Pickrell et al.

This study focuses on the development of reinforcement learning based techniques for the design of microelectronic components under multiphysics constraints. While traditional design approaches based on global optimization approaches are effective when dealing with a small number of design parameters, as the complexity of the solution space and of the constraints increases different techniques are needed. This is an important reason that makes the design and optimization of microelectronic components (characterized by large solution space and multiphysics constraints) very challenging for traditional methods. By taking as prototypical elements an application-specific integrated circuit (ASIC) and a heterogeneously integrated (HI) interposer, we develop and numerically test an optimization framework based on reinforcement learning (RL). More specifically, we consider the optimization of the bonded interconnect geometry for an ASIC chip as well as the placement of components on a HI interposer while satisfying thermoelastic and design constraints. This placement problem is particularly interesting because it features a high-dimensional solution space.

Siddharth Nair, Timothy F. Walsh, Greg Pickrell et al.

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution operator for different computational domains is a problem of general importance for a variety of engineering applications. To this end, we propose a physics-informed deep operator network (DeepONet) capable of predicting the scattered pressure field for arbitrarily shaped scatterers using a geometric parameterization approach based on non-uniform rational B-splines (NURBS). This approach also results in parsimonious representations of non-trivial scatterer geometries. In contrast to existing physics-based approaches that require model re-evaluation when changing the computational domains, our trained model is capable of learning solution operator that can approximate physically-consistent scattered pressure field in just a few seconds for arbitrary rigid scatterer shapes; it follows that the computational time for forward simulations can improve (i.e. be reduced) by orders of magnitude in comparison to the traditional forward solvers. In addition, this approach can evaluate the scattered pressure field without the need for labeled training data. After presenting the theoretical approach, a comprehensive numerical study is also provided to illustrate the remarkable ability of this approach to simulate the acoustic pressure fields resulting from arbitrary combinations of arbitrary scatterer geometries. These results highlight the unique generalization capability of the proposed operator learning approach.