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Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems for the steady state Navier-Stokes equations by combining deep neural networks and numerical PDE schemes. Our approach expresses numerical simulation as a computational graph with differentiable operators. We then solve inverse problems by constrained optimization, using gradients calculated from the computational graph with reverse-mode automatic differentiation. This technique enables us to model unknown physical properties using deep neural networks and embed them into the PDE model. Specifically, we express the Newton's iteration to solve the highly nonlinear Navier-Stokes equations as a computational graph. We demonstrate the effectiveness of our method by computing spatially-varying viscosity and conductivity fields with deep neural networks (DNNs) and training DNNs using partial observations of velocity fields. We show that DNNs are capable of modeling complex spatially-varying physical field with sparse and noisy data. We implement our method using ADCME, a library for solving inverse modeling problems in scientific computing using automatic differentiation.

A high density 5V-only flash memory array with sector erase mode is presented. It features a new triple poly splitgate source-side-injection cell in a contactless array to achieve small cell size, high programming efficiency, high cell current, with no over-erase concerns. The array design and its operating conditions in various modes are discussed. Various disturb reduction techniques, array performance and speed improvement schemes are presented. INTRODUCTIONThe flash memory technology is becoming technology of choice among other memory technologies, due to its capability to replace magnetic disk media (1). Split-gate source-side-injection cell is specially loolung very promising to achieve very high density, low power and 5V/3.3V-only flash memory. This cell has very high programming efficiency and very low write currents. The write currents can be optimized to be as low as luA and the read currents can be as high as 130uA for a cell size of 5 . 6~~2 on a 0.8um technology. The original paper by Kamiya et al., provided

Over the last few decades, existing Partial Differential Equation (PDE) solvers have demonstrated a tremendous success in solving complex, non-linear PDEs. Although accurate, these PDE solvers are computationally costly. With the advances in Machine Learning (ML) technologies, there has been a significant increase in the research of using ML to solve PDEs. The goal of this work is to develop an ML-based PDE solver, that couples important characteristics of existing PDE solvers with ML technologies. The two solver characteristics that have been adopted in this work are: 1) the use of discretization-based schemes to approximate spatio-temporal partial derivatives and 2) the use of iterative algorithms to solve linearized PDEs in their discrete form. In the presence of highly non-linear, coupled PDE solutions, these strategies can be very important in achieving good accuracy, better stability and faster convergence. Our ML-solver, DiscretizationNet, employs a generative CNN-based encoderdecoder model with PDE variables as both input and output features. During training, the discretization schemes are implemented inside the computational graph to enable faster GPU computation of PDE residuals, which are used to update network weights that result into converged solutions. A novel iterative capability is implemented during the network training to improve the stability and convergence of the ML-solver. The ML-Solver is demonstrated to solve the steady, incompressible Navier-Stokes equations in 3-D for several cases such as, lid-driven cavity, flow past a cylinder and conjugate heat transfer.

A highly reliable and scalable non-volatile embedded memory cell and technology is described. This embedded technology operates at very low power, and has minimal impact on the analog and digital components used in the SoC design. The main objective of this technology development was to achieve high reliability and high data retention for automotive applications over the extended temperature range from -40 O to 150 O C. A wider range, from -55 O to 180 O C, has been achieved in manufacturing. Full Cell, and memory module functionality, and data retention of over 30 years for the automotive temperature range have been achieved. Write cycling of over 200K writes (tested up to180 O C) over the design temperature range has also been achieved. The memory cell and the technology is optimized to operate at very low voltage and consume very low power. The applications requiring high data retention (>50 years), over the industrial or automotive temperature range can be well served with this technology. The data confirms that this technology is a highly manufacturable and a reliable technology for the embedded Non-Volatile memory applications. The data presented is based on a 0.35μm CMOS technology implementation.