Related papers: Deep set based operator learning with uncertainty …

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Predicting quantum operator matrices such as Hamiltonian, overlap, and density matrices in the density functional theory (DFT) framework is crucial for material science. Current methods often focus on individual operators and struggle with…

Recent performance breakthroughs in Artificial intelligence (AI) and Machine learning (ML), especially advances in Deep learning (DL), the availability of powerful, easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch.), and…

Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no…

In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question.…

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical…

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…

Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine…

We are interested in estimating the uncertainties of deep neural networks, which play an important role in many scientific and engineering problems. In this paper, we present a striking new finding that an ensemble of neural networks with…

Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Reconstructing high-fidelity fluid flow fields from sparse sensor measurements is vital for many science and engineering applications but remains challenging because of dimensional disparities between state and observational spaces. Due to…