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Decision-focused learning is a promising development for contextual optimisation. It enables us to train prediction models that reflect the contextual sensitivity structure of the problem. However, there have been limited attempts to extend…

Optimization and Control · Mathematics 2023-12-21 Egon Peršak , Miguel F. Anjos

Evolutionary algorithms are increasingly recognised as a viable computational approach for the automated optimisation of deep neural networks (DNNs) within artificial intelligence. This method extends to the training of DNNs, an approach…

Neural and Evolutionary Computing · Computer Science 2024-03-29 Fergal Stapleton , Brendan Cody-Kenny , Edgar Galván

Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…

Computational Physics · Physics 2025-09-05 Chenkai Mao , Jonathan A. Fan

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…

Numerical Analysis · Mathematics 2020-03-03 Liang Yan , Tao Zhou

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

Machine Learning · Computer Science 2019-06-06 Dennis Wei , Sanjeeb Dash , Tian Gao , Oktay Günlük

Existing rule-based explanations for Graph Neural Networks (GNNs) provide global interpretability but often optimize and assess fidelity in an intermediate, uninterpretable concept space, overlooking grounding quality for end users in the…

Machine Learning · Computer Science 2026-03-18 Chuqin Geng , Ziyu Zhao , Zhaoyue Wang , Haolin Ye , Yuhe Jiang , Xujie Si

A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods…

Computational Engineering, Finance, and Science · Computer Science 2025-10-28 Jiachen Guo , Chanwook Park , Xiaoyu Xie , Zhongsheng Sang , Gregory J. Wagner , Wing Kam Liu

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts.…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

Machine Learning · Statistics 2019-01-16 Yibo Yang , Paris Perdikaris

Graph Neural Networks (GNNs) have shown remarkable effectiveness in capturing abundant information in graph-structured data. However, the black-box nature of GNNs hinders users from understanding and trusting the models, thus leading to…

Machine Learning · Computer Science 2022-07-25 Jiaxuan Xie , Yezi Liu , Yanning Shen

We propose a novel training method that integrates rules into deep learning, in a way the strengths of the rules are controllable at inference. Deep Neural Networks with Controllable Rule Representations (DeepCTRL) incorporates a rule…

Machine Learning · Computer Science 2021-11-18 Sungyong Seo , Sercan O. Arik , Jinsung Yoon , Xiang Zhang , Kihyuk Sohn , Tomas Pfister

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many…

Interpreting the decision logic behind effective deep convolutional neural networks (CNN) on images complements the success of deep learning models. However, the existing methods can only interpret some specific decision logic on individual…

Computer Vision and Pattern Recognition · Computer Science 2021-08-24 Peter Cho-Ho Lam , Lingyang Chu , Maxim Torgonskiy , Jian Pei , Yong Zhang , Lanjun Wang

Explainable AI is a crucial component for edge services, as it ensures reliable decision making based on complex AI models. Surrogate models are a prominent approach of XAI where human-interpretable models, such as a linear regression…

Machine Learning · Computer Science 2025-03-12 Foivos Charalampakos , Thomas Tsouparopoulos , Iordanis Koutsopoulos

Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian…

Machine Learning · Computer Science 2019-07-02 Jan Niclas Reimann , Andreas Schwung

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

Machine Learning · Computer Science 2021-10-27 Mike Wu , Noah Goodman , Stefano Ermon

The success of recent deep convolutional neural networks (CNNs) depends on learning hidden representations that can summarize the important factors of variation behind the data. However, CNNs often criticized as being black boxes that lack…

Computer Vision and Pattern Recognition · Computer Science 2018-06-27 Bolei Zhou , David Bau , Aude Oliva , Antonio Torralba

Learning an explainable classifier often results in low accuracy model or ends up with a huge rule set, while learning a deep model is usually more capable of handling noisy data at scale, but with the cost of hard to explain the result and…

Artificial Intelligence · Computer Science 2022-11-11 Yuanlong Li , Gaopan Huang , Min Zhou , Chuan Fu , Honglin Qiao , Yan He

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

Machine Learning · Statistics 2019-05-02 Shaoxing Mo , Yinhao Zhu , Nicholas Zabaras , Xiaoqing Shi , Jichun Wu