Related papers: Probabilistic partition of unity networks: cluster…
We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the…
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity and monomials. Motivated by this, we propose partition of…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…
Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…
This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions.…
Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model…
The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…
Structure learning of Bayesian networks has always been a challenging problem. Nowadays, massive-size networks with thousands or more of nodes but fewer samples frequently appear in many areas. We develop a divide-and-conquer framework,…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
Motivated by the need to identify erroneous disparity assignments, various approaches for uncertainty and confidence estimation of dense stereo matching have been presented in recent years. As in many other fields, especially deep learning…