The 2048 mesh point high-resolution solution is generated using the Fourier-Galerkin spectral method [41] with the 4th order Runge-Kutta method for time stepping. From the box-filtered initial condition, the 32-point low-resolution solution is conducted using central differencing for the spatial derivatives. This choice does not introduce additional artificial viscosity; thus, the solution without closure is naturally unstable. In this setting, u can be regarded as fully resolved, thus the numerical residual r(u), defined in Eq.(10),iszero. Forthereacting flow simulation task, the different variables in the input q are normalized to the same order of magnitude.

Energy consumption is a growing concern in several fields, from mobile devices to large data centers. Developers need detailed data on the energy consumption of their software to mitigate consumption issues. Previous approaches have a broader focus, such as on specific functions or programs, rather than source code statements. They primarily focus on estimating the CPU's energy consumption using point estimates, thereby disregarding other hardware effects and limiting their use for statistical reasoning and explainability. We developed a novel methodology to address the limitations of measuring only the CPU's consumption and using point estimates, focusing on predicting the energy usage of statically typed JVM-based programming languages, such as Java and Scala. We measure the energy consumption of Bytecode patterns, the translation from the programming language's source code statement to their Java Bytecode representation. With the energy measurements, we construct a statistical model using Bayesian statistics, which allows us to predict the energy consumption through statistical distributions and analyze individual factors. The model includes three factors we obtain statically from the code: data size, data type, operation, and one factor about the hardware platform the code executes on: device. To validate our methodology, we implemented it for Java and evaluated its energy predictions on unseen programs. We observe that all four factors are influential, notably that two devices of the same model may differ in energy consumption and that the operations and data types cause consumption differences. The experiments also show that the energy prediction of programs closely follows the program's real energy consumption, validating our approach. Our work presents a methodology for constructing an energy model that future work, such as verification tools, can use for their energy estimates.

Multimodal large language models suffer from substantial inference overhead since multimodal KV Cache grows proportionally with the visual input length. Existing multimodal KV Cache compression methods mostly rely on attention score to reduce cache size, which makes them are incompatible with established efficient attention kernels (e.g., FlashAttention) and ignores the contribution of value vectors to the attention output. In this work, we revisit multimodal KV Cache compression from the perspective of the KV matrices' distribution. First, we observe that frequency-domain energy of multimodal KV matrices is predominantly concentrated in low-frequency and extract this principal energy via a low-pass filter. Further, we find that removing KV pairs that deviate substantially from this principal energy leads to a pronounced performance drop, which we define as Outlier KVs. Considering Outlier KVs are more likely to encode features critical for inference, we propose FlashCache, a frequency-domain-guided, Outlier-KV-aware KV Cache compression framework. First, we introduce an Outlier KV Recognition Module that models the principal component of multimodal KV matrices in the frequency domain and preferentially retains KV pairs that significantly deviate from it. Furthermore, Dynamic Budget Allocation Module is designed to adaptively determine the per-layer KV Cache size to retain more Outlier KVs. Experiments on multiple MLLMs and benchmarks demonstrate that FlashCache outperforms state-of-the-art multimoal KV compression methods, achieving up to 1.69 times faster decoding with 80% lower KV memory usage while maintaining task performance.

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact scientific applications. A promising approach towards this challenge is the design of amortized samplers that borrow key ideas, such as probability path design, from state-of-the-art generative diffusion models. However, all existing diffusion-based samplers remain unable to draw samples from distributions at the scale of even simple molecular systems. In this paper, we propose Progressive Inference-Time Annealing (PITA), a novel framework to learn diffusion-based samplers that combines two complementary interpolation techniques: I.) Annealing of the Boltzmann distribution and II.) Diffusion smoothing. PITA trains a sequence of diffusion models from high to low temperatures by sequentially training each model at progressively higher temperatures, leveraging engineered easy access to samples of the temperature-annealed target density. In the subsequent step, PITA enables simulating the trained diffusion model to procure training samples at a lower temperature for the next diffusion model through inference-time annealing using a novel Feynman-Kac PDE combined with Sequential Monte Carlo. Empirically, PITA enables, for the first time, equilibrium sampling of N-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates with dramatically lower energy function evaluations. Code available at: https://github.com/taraak/pita

Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to transform a simple prior into a distribution that can be reweighted to match the target using sample likelihoods. Despite the elegance of this approach, obtaining these likelihoods requires computing costly Jacobians during integration, which is impractical for large molecular systems. To overcome this difficulty, we train an energy-based model (EBM) to approximate likelihoods using both noise contrastive estimation (NCE) and score matching, which we show outperforms the use of either objective in isolation. On 2d synthetic systems where failure can be easily visualized, NCE improves mode weighting relative to score matching alone. On alanine dipeptide, our method yields free energy profiles and energy distributions that closely match those obtained using exact likelihoods while achieving $100\times$ faster inference. By training on multiple dipeptide systems, we show that our approach also exhibits effective transfer learning, generalizing to new systems at inference time and achieving at least a $6\times$ speedup over standard MD. While many recent efforts in generative modeling have prioritized models with fast sampling, our work demonstrates the design of models with accelerated likelihoods, enabling the application of reweighting schemes that ensure unbiased Boltzmann statistics at scale. Our code is available at https://github.com/RishalAggarwal/BoltzNCE.

Diffractive neural networks leverage the high-dimensional characteristics of electromagnetic (EM) fields for high-throughput computing. However, the existing architectures face challenges in integrating large-scale multidimensional metasurfaces with precise network training and haven't utilized multidimensional EM field coding scheme for super-resolution sensing. Here, we propose diffractive meta-neural networks (DMNNs) for accurate EM field modulation through metasurfaces, which enable multidimensional multiplexing and coding for multi-task learning and high-throughput super-resolution direction of arrival estimation. DMNN integrates pre-trained mini-metanets to characterize the amplitude and phase responses of meta-atoms across different polarizations and frequencies, with structure parameters inversely designed using the gradient-based meta-training. For wide-field super-resolution angle estimation, the system simultaneously resolves azimuthal and elevational angles through x and y-polarization channels, while the interleaving of frequency-multiplexed angular intervals generates spectral-encoded optical super-oscillations to achieve full-angle high-resolution estimation. Post-processing lightweight electronic neural networks further enhance the performance. Experimental results validate that a three-layer DMNN operating at 27 GHz, 29 GHz, and 31 GHz achieves $\sim7\times$ Rayleigh diffraction-limited angular resolution (0.5$^\circ$), a mean absolute error of 0.048$^\circ$ for two incoherent targets within a $\pm 11.5^\circ$ field of view, and an angular estimation throughput an order of magnitude higher (1917) than that of existing methods. The proposed architecture advances high-dimensional photonic computing systems by utilizing inherent high-parallelism and all-optical coding methods for ultra-high-resolution, high-throughput applications.

Oceanic processes at fine scales are crucial yet difficult to observe accurately due to limitations in satellite and in-situ measurements. The Surface Water and Ocean Topography (SWOT) mission provides high-resolution Sea Surface Height (SSH) data, though noise patterns often obscure fine scale structures. Current methods struggle with noisy data or require extensive supervised training, limiting their effectiveness on real-world observations. We introduce SIMPGEN (Simulation-Informed Metric and Prior for Generative Ensemble Networks), an unsupervised adversarial learning framework combining real SWOT observations with simulated reference data. SIMPGEN leverages wavelet-informed neural metrics to distinguish noisy from clean fields, guiding realistic SSH reconstructions. Applied to SWOT data, SIMPGEN effectively removes noise, preserving fine-scale features better than existing neural methods. This robust, unsupervised approach not only improves SWOT SSH data interpretation but also demonstrates strong potential for broader oceanographic applications, including data assimilation and super-resolution.

Modern Imaging Atmospheric Cherenkov Telescopes (IACTs) generate a huge amount of data that must be classified automatically, ideally in real time. Currently, machine learning-based solutions are increasingly being used to solve classification problems. However, these classifiers require proper training data sets to work correctly. The problem with training neural networks on real IACT data is that these data need to be pre-labeled, whereas such labeling is difficult and its results are estimates. In addition, the distribution of incoming events is highly imbalanced. Firstly, there is an imbalance in the types of events, since the number of detected gamma quanta is significantly less than the number of protons. Secondly, the energy distribution of particles of the same type is also imbalanced, since high-energy particles are extremely rare. This imbalance results in poorly trained classifiers that, once trained, do not handle rare events correctly. Using only conventional Monte Carlo event simulation methods to solve this problem is possible, but extremely resource-intensive and time-consuming. To address this issue, we propose to perform data augmentation with artificially generated events of the desired type and energy using conditional generative adversarial networks (cGANs), distinguishing classes by energy values. In the paper, we describe a simple algorithm for generating balanced data sets using cGANs. Thus, the proposed neural network model produces both imbalanced data sets for physical analysis as well as balanced data sets suitable for training other neural networks.

Graph neural networks (GNNs) have shown promise in integrating protein-protein interaction (PPI) networks for identifying cancer genes in recent studies. However, due to the insufficient modeling of the biological information in PPI networks, more faithfully depiction of complex protein interaction patterns for cancer genes within the graph structure remains largely unexplored. This study takes a pioneering step toward bridging biological anomalies in protein interactions caused by cancer genes to statistical graph anomaly. We find a unique graph anomaly exhibited by cancer genes, namely weight heterogeneity, which manifests as significantly higher variance in edge weights of cancer gene nodes within the graph. Additionally, from the spectral perspective, we demonstrate that the weight heterogeneity could lead to the "flattening out" of spectral energy, with a concentration towards the extremes of the spectrum. Building on these insights, we propose the HIerarchical-Perspective Graph Neural Network (HIPGNN) that not only determines spectral energy distribution variations on the spectral perspective, but also perceives detailed protein interaction context on the spatial perspective. Extensive experiments are conducted on two reprocessed datasets STRINGdb and CPDB, and the experimental results demonstrate the superiority of HIPGNN.