Related papers: Learning Geometry: A Framework for Building Adapti…
Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be…
This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a…
Continual learning is an emerging paradigm in machine learning, wherein a model is exposed in an online fashion to data from multiple different distributions (i.e. environments), and is expected to adapt to the distribution change.…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
We consider a class of a nested optimization problems involving inner and outer objectives. We observe that by taking into explicit account the optimization dynamics for the inner objective it is possible to derive a general framework that…
When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…
Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little…
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…
We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties.…
Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Deep learning has been widely used in various applications from different fields such as computer vision, natural language processing, etc. However, the training models are often manually developed via many costly experiments. This manual…
One frequently wishes to learn a range of similar tasks as efficiently as possible, re-using knowledge across tasks. In artificial neural networks, this is typically accomplished by conditioning a network upon task context by injecting…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…
Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a…
Structural optimization (topology, shapes, sizing) is an important tool for facilitating the emergence of new concepts in structural design. Normally, topology optimization is carried out at the early stage of design and then shape and…