Deep Learning (DL) models processing images to recognize the health state of large infrastructure components can exhibit biases and rely on non-causal shortcuts. eXplainable Artificial Intelligence (XAI) can address these issues but manually analyzing explanations generated by XAI techniques is time-consuming and prone to errors. This work proposes a novel framework that combines post-hoc explanations with semi-supervised learning to automatically identify anomalous explanations that deviate from those of correctly classified images and may therefore indicate model abnormal behaviors. This significantly reduces the workload for maintenance decision-makers, who only need to manually reclassify images flagged as having anomalous explanations. The proposed framework is applied to drone-collected images of insulator shells for power grid infrastructure monitoring, considering two different Convolutional Neural Networks (CNNs), GradCAM explanations and Deep Semi-Supervised Anomaly Detection. The average classification accuracy on two faulty classes is improved by 8% and maintenance operators are required to manually reclassify only 15% of the images. We compare the proposed framework with a state-of-the-art approach based on the faithfulness metric: the experimental results obtained demonstrate that the proposed framework consistently achieves F_1 scores larger than those of the faithfulness-based approach. Additionally, the proposed framework successfully identifies correct classifications that result from non-causal shortcuts, such as the presence of ID tags printed on insulator shells.

In real-world scenarios, achieving domain adaptation and generalization poses significant challenges, as models must adapt to or generalize across unknown target distributions. Extending these capabilities to unseen multimodal distributions, i.e., multimodal domain adaptation and generalization, is even more challenging due to the distinct characteristics of different modalities. Significant progress has been made over the years, with applications ranging from action recognition to semantic segmentation. Besides, the recent advent of large-scale pre-trained multimodal foundation models, such as CLIP, has inspired works leveraging these models to enhance adaptation and generalization performances or adapting them to downstream tasks. This survey provides the first comprehensive review of recent advances from traditional approaches to foundation models, covering: (1) Multimodal domain adaptation; (2) Multimodal test-time adaptation; (3) Multimodal domain generalization; (4) Domain adaptation and generalization with the help of multimodal foundation models; and (5) Adaptation of multimodal foundation models. For each topic, we formally define the problem and thoroughly review existing methods. Additionally, we analyze relevant datasets and applications, highlighting open challenges and potential future research directions. We maintain an active repository that contains up-to-date literature at https://github.com/donghao51/Awesome-Multimodal-Adaptation.

Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online search methods and pre-trained transformer models. Additionally, current state-of-the-art approaches typically do not consider the integration of domain experts' prior knowledge and do not support iterative interactions with the model during the equation discovery process. To address these challenges, we propose the Symbolic Q-network (Sym-Q), an advanced interactive framework for large-scale symbolic regression. Unlike previous large-scale transformer-based SR approaches, Sym-Q leverages reinforcement learning without relying on a transformer-based decoder. This formulation allows the agent to learn through offline reinforcement learning using any type of tree encoder, enabling more efficient training and inference. Furthermore, we propose a co-design mechanism, where the reinforcement learning-based Sym-Q facilitates effective interaction with domain experts at any stage of the equation discovery process. Users can dynamically modify generated nodes of the expression, collaborating with the agent to tailor the mathematical expression to best fit the problem and align with the assumed physical laws, particularly when there is prior partial knowledge of the expected behavior. Our experiments demonstrate that the pre-trained Sym-Q surpasses existing SR algorithms on the challenging SSDNC benchmark. Moreover, we experimentally show on real-world cases that its performance can be further enhanced by the interactive co-design mechanism, with Sym-Q achieving greater performance gains than other state-of-the-art models. Our reproducible code is available at https://github.com/EPFL-IMOS/Sym-Q.

Test-time adaptation (TTA) has demonstrated significant potential in addressing distribution shifts between training and testing data. Open-set test-time adaptation (OSTTA) aims to adapt a source pre-trained model online to an unlabeled target domain that contains unknown classes. This task becomes more challenging when multiple modalities are involved. Existing methods have primarily focused on unimodal OSTTA, often filtering out low-confidence samples without addressing the complexities of multimodal data. In this work, we present Adaptive Entropy-aware Optimization (AEO), a novel framework specifically designed to tackle Multimodal Open-set Test-time Adaptation (MM-OSTTA) for the first time. Our analysis shows that the entropy difference between known and unknown samples in the target domain strongly correlates with MM-OSTTA performance. To leverage this, we propose two key components: Unknown-aware Adaptive Entropy Optimization (UAE) and Adaptive Modality Prediction Discrepancy Optimization (AMP). These components enhance the model's ability to distinguish unknown class samples during online adaptation by amplifying the entropy difference between known and unknown samples. To thoroughly evaluate our proposed methods in the MM-OSTTA setting, we establish a new benchmark derived from existing datasets. This benchmark includes two downstream tasks - action recognition and 3D semantic segmentation - and incorporates five modalities: video, audio, and optical flow for action recognition, as well as LiDAR and camera for 3D semantic segmentation. Extensive experiments across various domain shift scenarios demonstrate the efficacy and versatility of the AEO framework. Additionally, we highlight the strong performance of AEO in long-term and continual MM-OSTTA settings, both of which are challenging and highly relevant to real-world applications. This underscores AEO's robustness and adaptability in dynamic environments. Our source code is available at https://github.com/donghao51/AEO. Test-time adaptation (TTA) significantly enhances the robustness and adaptability of machine learning models by enabling a source pre-trained model to adapt to target domains experiencing distribution shifts (Wang et al., 2021).

While many physical and engineering processes are most effectively described by non-linear symbolic models, existing non-linear symbolic regression (SR) methods are restricted to a limited set of continuous algebraic functions, thereby limiting their applicability to discover higher order non-linear differential relations. In this work, we introduce the Neural Operator-based symbolic Model approximaTion and discOvery (NOMTO) method, a novel approach to symbolic model discovery that leverages Neural Operators to encompass a broad range of symbolic operations. We demonstrate that NOMTO can successfully identify symbolic expressions containing elementary functions with singularities, special functions, and derivatives. Additionally, our experiments demonstrate that NOMTO can accurately rediscover second-order non-linear partial differential equations. It provides a powerful and flexible tool for model discovery, capable of capturing complex relations in a variety of physical systems. Many physical and engineering processes are most effectively described by concise mathematical expressions derived through meticulous observation and analysis. The accuracy of these models is highly dependent on the quality and quantity of available data. With the emergence of large-scale datasets across diverse physical and engineering domains, deriving compact mathematical models in the form of symbolic expressions has become increasingly attainable. This methodology, known as symbolic regression (SR), aims to identify mathematical expressions that most accurately represent given datasets. SR has become indispensable in fields such as physics, biology, and engineering, where it advances knowledge and fosters innovation by uncovering underlying principles and facilitating the development of interpretable predictive models. In recent years, deep learning-based approaches have significantly advanced the field of SR by leveraging neural networks to identify mathematical expressions directly from data.

Accurate, interpretable, and real-time modeling of multi-body dynamical systems is essential for predicting behaviors and inferring physical properties in natural and engineered environments. Traditional physics-based models face scalability challenges and are computationally demanding, while data-driven approaches like Graph Neural Networks (GNNs) often lack physical consistency, interpretability, and generalization. In this paper, we propose Dynami-CAL GraphNet, a Physics-Informed Graph Neural Network that integrates the learning capabilities of GNNs with physics-based inductive biases to address these limitations. Dynami-CAL GraphNet enforces pairwise conservation of linear and angular momentum for interacting nodes using edge-local reference frames that are equivariant to rotational symmetries, invariant to translations, and equivariant to node permutations. This design ensures physically consistent predictions of node dynamics while offering interpretable, edge-wise linear and angular impulses resulting from pairwise interactions. Evaluated on a 3D granular system with inelastic collisions, Dynami-CAL GraphNet demonstrates stable error accumulation over extended rollouts, effective extrapolations to unseen configurations, and robust handling of heterogeneous interactions and external forces. Dynami-CAL GraphNet offers significant advantages in fields requiring accurate, interpretable, and real-time modeling of complex multi-body dynamical systems, such as robotics, aerospace engineering, and materials science. By providing physically consistent and scalable predictions that adhere to fundamental conservation laws, it enables the inference of forces and moments while efficiently handling heterogeneous interactions and external forces. This makes it invaluable for designing control systems, optimizing mechanical processes, and analyzing dynamic behaviors in both natural and engineered systems.

Over the last decade, graph neural networks (GNNs) have made significant progress in numerous graph machine learning tasks. In real-world applications, where domain shifts occur and labels are often unavailable for a new target domain, graph domain adaptation (GDA) approaches have been proposed to facilitate knowledge transfer from the source domain to the target domain. Previous efforts in tackling distribution shifts across domains have mainly focused on aligning the node embedding distributions generated by the GNNs in the source and target domains. However, as the core part of GDA approaches, the impact of the underlying GNN architecture has received limited attention. In this work, we explore this orthogonal direction, i.e., how to facilitate GDA with architectural enhancement. In particular, we consider a class of GNNs that are designed explicitly based on optimization problems, namely unfolded GNNs (UGNNs), whose training process can be represented as bi-level optimization. Empirical and theoretical analyses demonstrate that when transferring from the source domain to the target domain, the lower-level objective value generated by the UGNNs significantly increases, resulting in an increase in the upper-level objective as well. Motivated by this observation, we propose a simple yet effective strategy called cascaded propagation (CP), which is guaranteed to decrease the lower-level objective value. The CP strategy is widely applicable to general UGNNs, and we evaluate its efficacy with three representative UGNN architectures. Extensive experiments on five real-world datasets demonstrate that the UGNNs integrated with CP outperform state-of-the-art GDA baselines.

Open-set Domain Adaptation (OSDA) aims to adapt a model from a labeled source domain to an unlabeled target domain, where novel classes - also referred to as target-private unknown classes - are present. Source-free Open-set Domain Adaptation (SF-OSDA) methods address OSDA without accessing labeled source data, making them particularly relevant under privacy constraints. However, SF-OSDA presents significant challenges due to distribution shifts and the introduction of novel classes. Existing SF-OSDA methods typically rely on thresholding the prediction entropy of a sample to identify it as either a known or unknown class but fail to explicitly learn discriminative features for the target-private unknown classes. We propose Recall and Refine (RRDA), a novel SF-OSDA framework designed to address these limitations by explicitly learning features for target-private unknown classes. RRDA employs a two-step process. First, we enhance the model's capacity to recognize unknown classes by training a target classifier with an additional decision boundary, guided by synthetic samples generated from target domain features. This enables the classifier to effectively separate known and unknown classes. In the second step, we adapt the entire model to the target domain, addressing both domain shifts and improving generalization to unknown classes. Any off-the-shelf source-free domain adaptation method (e.g., SHOT, AaD) can be seamlessly integrated into our framework at this stage. Extensive experiments on three benchmark datasets demonstrate that RRDA significantly outperforms existing SF-OSDA and OSDA methods.

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.

The deployment of affordable Internet of Things (IoT) sensors for air pollution monitoring has increased in recent years due to their scalability and cost-effectiveness. However, accurately calibrating these sensors in uncontrolled environments remains a significant challenge. While expensive reference sensors can provide accurate ground truth data, they are often deployed on a limited scale due to high costs, leading to a scarcity of labeled data. In diverse urban environments, data distributions constantly shift due to varying factors such as traffic patterns, industrial activities, and weather conditions, which impact sensor readings. Consequently, traditional machine learning models -- despite their increasing deployment for environmental sensor calibration -- often struggle to provide reliable pollutant measurements across different locations due to domain shifts. To address these challenges, we propose a novel unsupervised domain adaptation (UDA) method specifically tailored for regression tasks on graph-structured data. Our approach leverages Graph Neural Networks (GNNs) to model the relationships between sensors. To effectively capture critical spatial-temporal interactions, we incorporate spatial-temporal graph neural networks (STGNNs), which extend GNNs by incorporating temporal dynamics. To handle the resulting larger embeddings, we propose a domain adaptation method using a closed-form solution inspired by the Tikhonov-regularized least-squares problem. This method leverages Cholesky decomposition and power iteration to align the subspaces between source and target domains. By aligning these subspaces, our approach allows low-cost IoT sensors to learn calibration parameters from expensive reference sensors. This facilitates reliable pollutant measurements in new locations without the need for additional costly equipment.