Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms---e.g., random forests, artificial neural networks (ANNs)---with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures. Empirically, we demonstrate that the proposed architecture, PhysGNN, promises accurate and fast soft tissue deformation approximations, and is competitive with the state-of-the-art (SOTA) algorithms while promising enhanced computational feasibility, therefore suitable for neurosurgical settings.

Y et, forecasting beyond the weather timescale is challenging because it deals with problems other than initial condition, including boundary interaction, butterfly effect, and our inherent lack of physical understanding.

Y et, forecasting beyond the weather timescale is challenging because it deals with problems other than initial condition, including boundary interaction, butterfly effect, and our inherent lack of physical understanding.

Battery health prognostics are critical for ensuring safety, efficiency, and sustainability in modern energy systems. However, it has been challenging to achieve accurate and robust prognostics due to complex battery degradation behaviors with nonlinearity, noise, capacity regeneration, etc. Existing data-driven models capture temporal degradation features but often lack knowledge guidance, which leads to unreliable long-term health prognostics. To overcome these limitations, we propose Karma, a knowledge-aware model with frequency-adaptive learning for battery capacity estimation and remaining useful life prediction. The model first performs signal decomposition to derive battery signals in different frequency bands. A dual-stream deep learning architecture is developed, where one stream captures long-term low-frequency degradation trends and the other models high-frequency short-term dynamics. Karma regulates the prognostics with knowledge, where battery degradation is modeled as a double exponential function based on empirical studies. Our dual-stream model is used to optimize the parameters of the knowledge with particle filters to ensure physically consistent and reliable prognostics and uncertainty quantification. Experimental study demonstrates Karma's superior performance, achieving average error reductions of 50.6% and 32.6% over state-of-the-art algorithms for battery health prediction on two mainstream datasets, respectively. These results highlight Karma's robustness, generalizability, and potential for safer and more reliable battery management across diverse applications.

ChaosBench is published under the open source GNU General Public License. Furthermore, we are committed to maintaining and preserving the ChaosBench benchmark. User feedback will be closely monitored via the GitHub issue tracker. Dataset: All our dataset, present and future (e.g., with more years, multi-resolution support, etc) are Here, we provide a detailed description on how to prepare the necessary data, perform training, and benchmark your own model. B.1 Data Preparation First, navigate to the repository directory and install the necessary dependencies.

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given basis functions. A major challenge in SINDy is the design of a library, which is a set of candidate basis functions, as the appropriate library is not trivial for many dynamical systems. To overcome this difficulty, this study proposes SINDy with library optimization mechanism (SINDy-LOM), which is a combination of the sparse regression technique and the novel learning strategy of the library. In the proposed approach, the basis functions are parametrized. The SINDy-LOM approach involves a two-layer optimization architecture: the inner-layer, in which the data-driven model is extracted as the sparse linear combination of the candidate basis functions, and the outer-layer, in which the basis functions are optimized from the viewpoint of the recursive long-term (RLT) prediction accuracy; thus, the library design is reformulated as the optimization of the parametrized basis functions. The resulting SINDy-LOM model has good interpretability and usability, as the proposed approach yields the parsimonious model. The library optimization mechanism significantly reduces user burden. The RLT perspective improves the reliability of the resulting model compared with the traditional SINDy approach that can only ensure the one-step-ahead prediction accuracy. The validity of the proposed approach is demonstrated by applying it to a diesel engine airpath system, which is a well-known complex industrial system.

Building energy modeling is a key tool for optimizing the performance of building energy systems. Historically, a wide spectrum of methods has been explored -- ranging from conventional physics-based models to purely data-driven techniques. Recently, hybrid approaches that combine the strengths of both paradigms have gained attention. These include strategies such as learning surrogates for physics-based models, modeling residuals between simulated and observed data, fine-tuning surrogates with real-world measurements, using physics-based outputs as additional inputs for data-driven models, and integrating the physics-based output into the loss function the data-driven model. Despite this progress, two significant research gaps remain. First, most hybrid methods focus on deterministic modeling, often neglecting the inherent uncertainties caused by factors like weather fluctuations and occupant behavior. Second, there has been little systematic comparison within a probabilistic modeling framework. This study addresses these gaps by evaluating five representative hybrid approaches for probabilistic building energy modeling, focusing on quantile predictions of building thermodynamics in a real-world case study. Our results highlight two main findings. First, the performance of hybrid approaches varies across different building room types, but residual learning with a Feedforward Neural Network performs best on average. Notably, the residual approach is the only model that produces physically intuitive predictions when applied to out-of-distribution test data. Second, Quantile Conformal Prediction is an effective procedure for calibrating quantile predictions in case of indoor temperature modeling.

Vehicle state estimation presents a fundamental challenge for autonomous driving systems, requiring both physical interpretability and the ability to capture complex nonlinear behaviors across diverse operating conditions. Traditional methodologies often rely exclusively on either physics-based or data-driven models, each with complementary strengths and limitations that become most noticeable during critical scenarios. This paper presents a novel consensus multi-model Kalman filter framework that integrates heterogeneous model types to leverage their complementary strengths while minimizing individual weaknesses. We introduce two distinct methodologies for handling covariance propagation in data-driven models: a Koopman operator-based linearization approach enabling analytical covariance propagation, and an ensemble-based method providing unified uncertainty quantification across model types without requiring pretraining. Our approach implements an iterative consensus fusion procedure that dynamically weighs different models based on their demonstrated reliability in current operating conditions. The experimental results conducted on an electric all-wheel-drive Equinox vehicle demonstrate performance improvements over single-model techniques, with particularly significant advantages during challenging maneuvers and varying road conditions, confirming the effectiveness and robustness of the proposed methodology for safety-critical autonomous driving applications.

--A fundamental challenge in car-following modeling lies in accurately representing the multi-scale complexity of driving behaviors, particularly the intra-driver heterogeneity where a single driver's actions fluctuate dynamically under varying conditions. While existing models, both conventional and data-driven, address behavioral heterogeneity to some extent, they often emphasize inter-driver heterogeneity or rely on simplified assumptions, limiting their ability to capture the dynamic heterogeneity of a single driver under different driving conditions. T o address this gap, we propose a novel data-driven car-following framework that systematically embeds discrete driving regimes (e.g., steady-state following, acceleration, cruising) into vehicular motion predictions. Leveraging high-resolution traffic trajectory datasets, the proposed hybrid deep learning architecture combines Gated Recurrent Units for discrete driving regime classification with Long Short-T erm Memory networks for continuous kinematic prediction, unifying discrete decision-making processes and continuous vehicular dynamics to comprehensively represent inter-and intra-driver heterogeneity. Driving regimes are identified using a bottom-up segmentation algorithm and Dynamic Time Warping, ensuring robust characterization of behavioral states across diverse traffic scenarios. Comparative analyses demonstrate that the framework significantly reduces prediction errors for acceleration (maximum MSE improvement reached 58.47%), speed, and spacing metrics while reproducing critical traffic phenomena, such as stop-and-go wave propagation and oscillatory dynamics. Understanding and modeling car-following behavior is fundamental to microscopic traffic flow research, serving as a bridge between individual driving dynamics and macro-level traffic phenomena.

We propose a data-driven, user-centric vehicle-to-grid (V2G) methodology based on multi-objective optimization to balance battery degradation and V2G revenue according to EV user preference. Given the lack of accurate and generalizable battery degradation models, we leverage input convex neural networks (ICNNs) to develop a data-driven degradation model trained on extensive experimental datasets. This approach enables our model to capture nonconvex dependencies on battery temperature and time while maintaining convexity with respect to the charging rate. Such a partial convexity property ensures that the second stage of our methodology remains computationally efficient. In the second stage, we integrate our data-driven degradation model into a multi-objective optimization framework to generate an optimal smart charging profile for each EV. This profile effectively balances the trade-off between financial benefits from V2G participation and battery degradation, controlled by a hyperparameter reflecting the user prioritization of battery health. Numerical simulations show the high accuracy of the ICNN model in predicting battery degradation for unseen data. Finally, we present a trade-off curve illustrating financial benefits from V2G versus losses from battery health degradation based on user preferences and showcase smart charging strategies under realistic scenarios.