Lift-and-Embed Learning Methods for Solving Scalar Hyperbolic Equations with Discontinuous Solutions
Unlike traditional mesh-based approximations of differential operators, machine learning methods, which exploit the automatic differentiation of neural networks, have attracted increasing attention for their potential to mitigate stability issues encountered in the numerical simulation of hyperbolic conservation laws. However, solutions to hyperbolic problems are often piecewise smooth, rendering the differential form invalid along discontinuity interfaces and limiting the effectiveness of standard learning approaches. In this work, we propose lift-and-embed learning methods for solving scalar hyperbolic equations with discontinuous solutions, which consist of (i) embedding the Rankine-Hugoniot jump condition within a higher-dimensional space through the inclusion of an augmented variable in the solution ansatz; (ii) utilizing physics-informed neural networks to manage the increased dimensionality and to address both linear and quasi-linear problems within a unified learning framework; and (iii) projecting the trained network solution back onto the original lower-dimensional plane to obtain the approximate solution. Besides, the location of discontinuity can be parametrized as extra model parameters and inferred concurrently with the training of network solution. With collocation points sampled on piecewise surfaces rather than distributed over the entire lifted space, we conduct numerical experiments on various benchmark problems to demonstrate the capability of our methods in resolving discontinuous solutions without spurious numerical smearing and oscillations.
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Effective modeling of group interactions and dynamic semantic intentions is crucial for forecasting behaviors like trajectories or movements. In complex scenarios like sports, agents' trajectories are influenced by group interactions and intentions, including team strategies and opponent actions. To this end, we propose a novel diffusion-based trajectory prediction framework that integrates group-level interactions into a conditional diffusion model, enabling the generation of diverse trajectories aligned with specific group activity. To capture dynamic semantic intentions, we frame group interaction prediction as a cooperative game, using Banzhaf interaction to model cooperation trends. We then fuse semantic intentions with enhanced agent embeddings, which are refined through both global and local aggregation. Furthermore, we expand the NBA SportVU dataset by adding human annotations of team-level tactics for trajectory and tactic prediction tasks. Extensive experiments on three widely-adopted datasets demonstrate that our model outperforms state-of-the-art methods. Our source code and data are available at //github.com/aurora-xin/Group2Int-trajectory.
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and limited in size such that quantum heuristics cannot be scaled to relevant problem sizes and are often outperformed by their classical counterparts. Moreover, if provably optimal solutions are desired, one has to resort to classical exact methods. As however quantum technologies may improve considerably in future, we demonstrate in this work how quantum heuristics with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems. To this end, we consider vehicle routing as prototypical NP-hard problem. We model the pricing and separation subproblems arising in a branch-price-and-cut algorithm as quadratic unconstrained binary optimization problems. This allows to use established quantum heuristics like quantum annealing or the quantum approximate optimization algorithm for their solution. A key feature of our algorithm is that it profits not only from the best solution returned by the quantum heuristic but from all solutions below a certain cost threshold, thereby exploiting the inherent randomness is quantum algorithms. Moreover, we reduce the requirements on quantum hardware since the subproblems, which are solved via quantum heuristics, are smaller than the original problem. We provide an experimental study comparing quantum annealing to simulated annealing and to established classical algorithms in our framework. While our hybrid quantum-classical approach is still outperformed by purely classical methods, our results reveal that both pricing and separation may be well suited for quantum heuristics if quantum hardware improves.
Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original geometric space, leading to high computational costs when the number of sample points is large. We present the Latent Neural Operator (LNO) solving PDEs in the latent space. In particular, we first propose Physics-Cross-Attention (PhCA) transforming representation from the geometric space to the latent space, then learn the operator in the latent space, and finally recover the real-world geometric space via the inverse PhCA map. Our model retains flexibility that can decode values in any position not limited to locations defined in the training set, and therefore can naturally perform interpolation and extrapolation tasks particularly useful for inverse problems. Moreover, the proposed LNO improves both prediction accuracy and computational efficiency. Experiments show that LNO reduces the GPU memory by 50%, speeds up training 1.8 times, and reaches state-of-the-art accuracy on four out of six benchmarks for forward problems and a benchmark for inverse problem. Code is available at //github.com/L-I-M-I-T/LatentNeuralOperator.
In applying deep learning for malware classification, it is crucial to account for the prevalence of malware evolution, which can cause trained classifiers to fail on drifted malware. Existing solutions to address concept drift use active learning. They select new samples for analysts to label and then retrain the classifier with the new labels. Our key finding is that the current retraining techniques do not achieve optimal results. These techniques overlook that updating the model with scarce drifted samples requires learning features that remain consistent across pre-drift and post-drift data. The model should thus be able to disregard specific features that, while beneficial for the classification of pre-drift data, are absent in post-drift data, thereby preventing prediction degradation. In this paper, we propose a new technique for detecting and classifying drifted malware that learns drift-invariant features in malware control flow graphs by leveraging graph neural networks with adversarial domain adaptation. We compare it with existing model retraining methods in active learning-based malware detection systems and other domain adaptation techniques from the vision domain. Our approach significantly improves drifted malware detection on publicly available benchmarks and real-world malware databases reported daily by security companies in 2024. We also tested our approach in predicting multiple malware families drifted over time. A thorough evaluation shows that our approach outperforms the state-of-the-art approaches.
Extracting time-varying latent variables from computational cognitive models is a key step in model-based neural analysis, which aims to understand the neural correlates of cognitive processes. However, existing methods only allow researchers to infer latent variables that explain subjects' behavior in a relatively small class of cognitive models. For example, a broad class of relevant cognitive models with analytically intractable likelihood is currently out of reach from standard techniques, based on Maximum a Posteriori parameter estimation. Here, we present an approach that extends neural Bayes estimation to learn a direct mapping between experimental data and the targeted latent variable space using recurrent neural networks and simulated datasets. We show that our approach achieves competitive performance in inferring latent variable sequences in both tractable and intractable models. Furthermore, the approach is generalizable across different computational models and is adaptable for both continuous and discrete latent spaces. We then demonstrate its applicability in real world datasets. Our work underscores that combining recurrent neural networks and simulation-based inference to identify latent variable sequences can enable researchers to access a wider class of cognitive models for model-based neural analyses, and thus test a broader set of theories.
A near-field wideband beamforming scheme is investigated for reconfigurable intelligent surface (RIS) assisted multiple-input multiple-output (MIMO) systems, in which a deep learning-based end-to-end (E2E) optimization framework is proposed to maximize the system spectral efficiency. To deal with the near-field double beam split effect, the base station is equipped with frequency-dependent hybrid precoding architecture by introducing sub-connected true time delay (TTD) units, while two specific RIS architectures, namely true time delay-based RIS (TTD-RIS) and virtual subarray-based RIS (SA-RIS), are exploited to realize the frequency-dependent passive beamforming at the RIS. Furthermore, the efficient E2E beamforming models without explicit channel state information are proposed, which jointly exploits the uplink channel training module and the downlink wideband beamforming module. In the proposed network architecture of the E2E models, the classical communication signal processing methods, i.e., polarized filtering and sparsity transform, are leveraged to develop a signal-guided beamforming network. Numerical results show that the proposed E2E models have superior beamforming performance and robustness to conventional beamforming benchmarks. Furthermore, the tradeoff between the beamforming gain and the hardware complexity is investigated for different frequency-dependent RIS architectures, in which the TTD-RIS can achieve better spectral efficiency than the SA-RIS while requiring additional energy consumption and hardware cost.
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, we consider full-scale approximations (FSAs) that combine predictive process methods and covariance tapering, thus approximating both global and local structures. We show how iterative methods can be used to reduce the computational costs for calculating likelihoods, gradients, and predictive distributions with FSAs. We introduce a novel preconditioner and show that it accelerates the conjugate gradient method's convergence speed and mitigates its sensitivity with respect to the FSA parameters and the eigenvalue structure of the original covariance matrix, and we demonstrate empirically that it outperforms a state-of-the-art pivoted Cholesky preconditioner. Further, we present a novel, accurate, and fast way to calculate predictive variances relying on stochastic estimations and iterative methods. In both simulated and real-world data experiments, we find that our proposed methodology achieves the same accuracy as Cholesky-based computations with a substantial reduction in computational time. Finally, we also compare different approaches for determining inducing points in predictive process and FSA models. All methods are implemented in a free C++ software library with high-level Python and R packages.
With the rising imaging resolution of handheld devices, existing multi-exposure image fusion algorithms struggle to generate a high dynamic range image with ultra-high resolution in real-time. Apart from that, there is a trend to design a manageable and editable algorithm as the different needs of real application scenarios. To tackle these issues, we introduce 3D LUT technology, which can enhance images with ultra-high-definition (UHD) resolution in real time on resource-constrained devices. However, since the fusion of information from multiple images with different exposure rates is uncertain, and this uncertainty significantly trials the generalization power of the 3D LUT grid. To address this issue and ensure a robust learning space for the model, we propose using a teacher-student network to model the uncertainty on the 3D LUT grid.Furthermore, we provide an editable mode for the multi-exposure image fusion algorithm by using the implicit representation function to match the requirements in different scenarios. Extensive experiments demonstrate that our proposed method is highly competitive in efficiency and accuracy.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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