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Accurate flight delay prediction is crucial for the secure and effective operation of the air traffic system. Recent advances in modeling inter-airport relationships present a promising approach for investigating flight delay prediction…

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

Discovering causal models from observational and interventional data is an important first step preceding what-if analysis or counterfactual reasoning. As has been shown before, the direction of pairwise causal relations can, under certain…

A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove,…

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…

This paper studies the problem of real-time fault recovery control for nonlinear control-affine systems subject to actuator loss of effectiveness faults and external disturbances. We derive a two-stage framework that combines causal…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…

We present a causal view on the robustness of neural networks against input manipulations, which applies not only to traditional classification tasks but also to general measurement data. Based on this view, we design a deep causal…

The problem of explaining the results produced by machine learning methods continues to attract attention. Neural network (NN) models, along with gradient boosting machines, are expected to be utilized even in tabular data with high…

Traditional Low-Light Image Enhancement (LLIE) methods primarily focus on uniform brightness adjustment, often neglecting instance-level semantic information and the inherent characteristics of different features. To address these…

Deep Learning models have shown success in a large variety of tasks by extracting correlation patterns from high-dimensional data but still struggle when generalizing out of their initial distribution. As causal engines aim to learn…

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…

Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random…

We address the problem of estimating causal effects from observational data in the presence of network confounding, a setting where both treatment assignment and observed outcomes of individuals may be influenced by their neighbors within a…

Causal set theory is an intrinsically nonlocal approach to quantum gravity, inheriting its nonlocality from Lorentzian nonlocality. This nonlocality causes problems in defining differential operators -- such as the d'Alembert operator, a…

Model quantization, which aims to compress deep neural networks and accelerate inference speed, has greatly facilitated the development of cumbersome models on mobile and edge devices. There is a common assumption in quantization methods…

Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators, and quantum causality between the involved events in an experiment is encoded in the corresponding pseudo-density operator. We study…

Causal probabilistic graph-based models have gained widespread utility, enabling the modeling of cause-and-effect relationships across diverse domains. With their rising adoption in new areas, such as automotive system safety and machine…