LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial discretization, and then serves to accelerate simulations with the same discretization. This discretization-dependence is restrictive. Becoming independent of a specific discretization would provide flexibility to mix and match mesh resolutions, connectivity, and type (tetrahedral, hexahedral) in training data; to accelerate simulations with novel discretizations unseen during training; and to accelerate adaptive simulations that temporally or parametrically change the discretization. We present a flexible, discretization-independent approach to reduced-order modeling. Like traditional ROM, we represent the configuration as a linear combination of displacement fields. Unlike traditional ROM, our displacement fields are continuous maps from every point on the reference domain to a corresponding displacement vector; these maps are represented as implicit neural fields. With linear continuous ROM (LiCROM), our training set can include multiple geometries undergoing multiple loading conditions, independent of their discretization. This opens the door to novel applications of reduced order modeling. We can now accelerate simulations that modify the geometry at runtime, for instance via cutting, hole punching, and even swapping the entire mesh. We can also accelerate simulations of geometries unseen during training. We demonstrate one-shot generalization, training on a single geometry and subsequently simulating various unseen geometries

Neural Stress Fields for Reduced-order Elastoplasticity and Fracture

We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X

Embedded Machine Learning: Emphasis on Hardware Accelerators and Approximate Computing for Tactile Data Processing

Machine Learning (ML) a subset of Artificial Intelligence (AI) is driving the industrial and technological revolution of the present and future. We envision a world with smart devices that are able to mimic human behavior (sense, process, and act) and perform tasks that at one time we thought could only be carried out by humans. The vision is to achieve such a level of intelligence with affordable, power-efficient, and fast hardware platforms. However, embedding machine learning algorithms in many application domains such as the internet of things (IoT), prostheses, robotics, and wearable devices is an ongoing challenge. A challenge that is controlled by the computational complexity of ML algorithms, the performance/availability of hardware platforms, and the application\u2019s budget (power constraint, real-time operation, etc.). In this dissertation, we focus on the design and implementation of efficient ML algorithms to handle the aforementioned challenges. First, we apply Approximate Computing Techniques (ACTs) to reduce the computational complexity of ML algorithms. Then, we design custom Hardware Accelerators to improve the performance of the implementation within a specified budget. Finally, a tactile data processing application is adopted for the validation of the proposed exact and approximate embedded machine learning accelerators. The dissertation starts with the introduction of the various ML algorithms used for tactile data processing. These algorithms are assessed in terms of their computational complexity and the available hardware platforms which could be used for implementation. Afterward, a survey on the existing approximate computing techniques and hardware accelerators design methodologies is presented. Based on the findings of the survey, an approach for applying algorithmic-level ACTs on machine learning algorithms is provided. Then three novel hardware accelerators are proposed: (1) k-Nearest Neighbor (kNN) based on a selection-based sorter, (2) Tensorial Support Vector Machine (TSVM) based on Shallow Neural Networks, and (3) Hybrid Precision Binary Convolution Neural Network (BCNN). The three accelerators offer a real-time classification with monumental reductions in the hardware resources and power consumption compared to existing implementations targeting the same tactile data processing application on FPGA. Moreover, the approximate accelerators maintain a high classification accuracy with a loss of at most 5%

Exploring the Use of Adaptively Restrained Particles for Graphics Simulations

International audienceIn this paper, we explore the use of Adaptively Restrained (AR) particles for graphics simulations. Contrary to previous methods, Adaptively Restrained Particle Simulations (ARPS) do not adapt time or space sampling, but rather switch the positional degrees of freedom of particles on and off, while letting their momenta evolve. Therefore, inter-particles forces do not have to be updated at each time step, in contrast with traditional methods that spend a lot of time there. We present the initial formulation of ARPS that was introduced for molecular dynamics simulations, and explore its potential for Computer Graphics applications: We first adapt ARPS to particle-based fluid simulations and propose an efficient incremental algorithm to update forces and scalar fields. We then introduce a new implicit integration scheme enabling to use ARPS for cloth simulation as well. Our experiments show that this new, simple strategy for adaptive simulations can provide significant speedups more easily than traditional adaptive models

Model Reduction of Muscle-Driven Tissue Models

Biomechanical simulations are a necessary tool for a proper understanding of biomechanics and hence are subject to intense research. One field that relies on this research is articulatory speech synthesis as it attempts to simulate the physics of the speech production process. Out of the many aspects involved, muscle driven tissue is one of the most important as it is required to simulate the deformable structures of the vocal tract. Modelling of muscle driven tissue requires continuum models of high complexity for the purpose of accuracy. On the other hand, time-efficient models are desirable in order to provide fast simulations which enable the user to test input parameters interactively. These requirements impose limitations on each other as the time-efficiency of a model is reduced with increasing complexity, hence techniques that can bridge the gap between these requirements are needed. This thesis attempts to bridge this gap through two major contributions. Model reduction techniques, that up until now have only been applied to inactive materials, have been implemented and tested for muscle driven tissue models. The implementation has been made in a general way to ensure that it can be used for biomechanical simulations in other fields than articulatory speech synthesis. In addition, the implementation has been made such that it can handle more advanced simulations than those investigated in this thesis. The simulations show acceptable but not ideal accuracy in both dynamic simulations and in measurements of equilibrium configurations. In addition, the reduced simulations using hyperreduction show good speedup for the more complex models investigated

3D object recognition without CAD models for industrial robot manipulation

In this work we present a new algorithm for 3D object recognition. The goal is to identify the correct position and orientation of complex objects without using a CAD model, input of main current systems. The approach we follow performs feature matching. The characteristics extracted belong only by shape information to achieve a system independent to brightness, colour or texture. Designing opportune settable parameters, we allow recognition also in presence of small deformation