Related papers: Operator Inference Aware Quadratic Manifolds with …

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…

Learning embedding spaces of suitable geometry is critical for representation learning. In order for learned representations to be effective and efficient, it is ideal that the geometric inductive bias aligns well with the underlying…

The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…

We propose a method for learning embeddings for few-shot learning that is suitable for use with any number of ways and any number of shots (shot-free). Rather than fixing the class prototypes to be the Euclidean average of sample…

Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction…

Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively…

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…

Learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes that preserve the…

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data…

One of the prevailing trends in the machine- and deep-learning community is to gravitate towards the use of increasingly larger models in order to keep pushing the state-of-the-art performance envelope. This tendency makes access to the…

Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…

Recent research has seen numerous supervised learning-based methods for 3D shape segmentation and remarkable performance has been achieved on various benchmark datasets. These supervised methods require a large amount of annotated data to…

Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This…

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

We introduce an unsupervised approach for constructing a global reference system by learning, in the ambient space, vector fields that span the tangent spaces of an unknown data manifold. In contrast to isometric objectives, which…

Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…

This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on Decision and Control and the…

In-hand object manipulation is challenging to simulate due to complex contact dynamics, non-repetitive finger gaits, and the need to indirectly control unactuated objects. Further adapting a successful manipulation skill to new objects with…

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…