Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this context, standard physical modeling-based approaches tend to be over-simplistic, inducing non-negligible errors. In this work, we introduce the APHYNITY framework, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists of decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model. The learning problem is carefully formulated such that the physical model explains as much of the data as possible, while the data-driven component only describes information that cannot be captured by the physical model; no more, no less. This not only provides the existence and uniqueness for this decomposition, but also ensures interpretability and benefit generalization. Experiments made on three important use cases, each representative of a different family of phenomena, i.e. reaction–diffusion equations, wave equations and the non-linear damped pendulum, show that APHYNITY can efficiently leverage approximate physical models to accurately forecast the evolution of the system and correctly identify relevant physical parameters. The code is available at https://github.com/yuan-yin/APHYNITY .

A crucial challenge in critical settings like medical diagnosis is making deep learning models used in decision-making systems interpretable. Efforts in Explainable Artificial Intelligence (XAI) are underway to address this challenge. Yet, many XAI methods are evaluated on broad classifiers and fail to address complex, real-world issues, such as medical diagnosis. In our study, we focus on enhancing user trust and confidence in automated AI decision-making systems, particularly for diagnosing skin lesions, by tailoring an XAI method to explain an AI model’s ability to identify various skin lesion types. We generate explanations using synthetic images of skin lesions as examples and counterexamples, offering a method for practitioners to pinpoint the critical features influencing the classification outcome. A validation survey involving domain experts, novices, and laypersons has demonstrated that explanations increase trust and confidence in the automated decision system. Furthermore, our exploration of the model’s latent space reveals clear separations among the most common skin lesion classes, a distinction that likely arises from the unique characteristics of each class and could assist in correcting frequent misdiagnoses by human professionals.

A key issue in critical contexts such as medical diagnosis is the interpretability of the deep learning models adopted in decision-making systems. Research in eXplainable Artificial Intelligence (XAI) is trying to solve this issue. However, often XAI approaches are only tested on generalist classifier and do not represent realistic problems such as those of medical diagnosis. In this paper, we aim at improving the trust and confidence of users towards automatic AI decision systems in the field of medical skin lesion diagnosis by customizing an existing XAI approach for explaining an AI model able to recognize different types of skin lesions. The explanation is generated through the use of synthetic exemplar and counter-exemplar images of skin lesions and our contribution offers the practitioner a way to highlight the crucial traits responsible for the classification decision. A validation survey with domain experts, beginners, and unskilled people shows that the use of explanations improves trust and confidence in the automatic decision system. Also, an analysis of the latent space adopted by the explainer unveils that some of the most frequent skin lesion classes are distinctly separated. This phenomenon may stem from the intrinsic characteristics of each class and may help resolve common misclassifications made by human experts.

Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this context, standard physical modeling based approaches tend to be over-simplistic, inducing non-negligible errors. In this work, we introduce the APHYNITY framework, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists in decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model. The learning problem is carefully formulated such that the physical model explains as much of the data as possible, while the data-driven component only describes information that cannot be captured by the physical model, no more, no less. This not only provides the existence and uniqueness for this decomposition, but also ensures interpretability and benefits generalization. Experiments made on three important use cases, each representative of a different family of phenomena, i.e. reaction-diffusion equations, wave equations and the non-linear damped pendulum, show that APHYNITY can efficiently leverage approximate physical models to accurately forecast the evolution of the system and correctly identify relevant physical parameters. Code is available at https://github.com/yuan-yin/APHYNITY .

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

When modeling dynamical systems from real-world data samples, the distribution of data often changes according to the environment in which they are captured, and the dynamics of the system itself vary from one environment to another. Generalizing across environments thus challenges the conventional frameworks. The classical settings suggest either considering data as i.i.d. and learning a single model to cover all situations or learning environment-specific models. Both are sub-optimal: the former disregards the discrepancies between environments leading to biased solutions, while the latter does not exploit their potential commonalities and is prone to scarcity problems. We propose LEADS, a novel framework that leverages the commonalities and discrepancies among known environments to improve model generalization. This is achieved with a tailored training formulation aiming at capturing common dynamics within a shared model while additional terms capture environment-specific dynamics. We ground our approach in theory, exhibiting a decrease in sample complexity with our approach and corroborate these results empirically, instantiating it for linear dynamics. Moreover, we concretize this framework for neural networks and evaluate it experimentally on representative families of nonlinear dynamics. We show that this new setting can exploit knowledge extracted from environment-dependent data and improves generalization for both known and novel environments. Code is available at https://github.com/yuan-yin/LEADS.