Related papers: DeepONet-Grid-UQ: A Trustworthy Deep Operator Fram…
We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two…
Failure trajectories, identifying the probable failure zones, and damage statistics are some of the key quantities of relevance in brittle fracture applications. High-fidelity numerical solvers that reliably estimate these relevant…
Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing…
Power demand forecasting is a critical task for achieving efficiency and reliability in power grid operation. Accurate forecasting allows grid operators to better maintain the balance of supply and demand as well as to optimize operational…
Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of…
Estimating uncertainty from deep neural networks is a widely used approach for detecting out-of-distribution (OoD) samples, which typically exhibit high predictive uncertainty. However, conventional methods such as Monte Carlo (MC) Dropout…
Development of an accurate, flexible, and numerically efficient uncertainty quantification (UQ) method is one of fundamental challenges in machine learning. Previously, a UQ method called DISCO Nets has been proposed (Bouchacourt et al.,…
Despite tremendous success of modern neural networks, they are known to be overconfident even when the model encounters inputs with unfamiliar conditions. Detecting such inputs is vital to preventing models from making naive predictions…
Accurate precipitation forecasts are crucial for applications such as flood management, agricultural planning, water resource allocation, and weather warnings. Despite advances in numerical weather prediction (NWP) models, they still…
Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…
Pathloss prediction is an essential component of wireless network planning. While ray tracing based methods have been successfully used for many years, they require significant computational effort that may become prohibitive with the…
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…
In this paper, we propose a DeepONet structure with causality to represent the causal linear operators between Banach spaces of time-dependent signals. The theorem of universal approximations to nonlinear operators proposed in…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…
We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…
Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…
Ensemble method is considered the gold standard for uncertainty quantification (UQ) in machine learning interatomic potentials (MLIPs). However, their high computational cost can limit its practicality. Alternative techniques, such as Monte…