Daily Papers

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is employed to provide the analysis state of the system, which is then used to estimate the model error. Finally, an equation-discovery technique, here the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, and closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

The continuous operation of Earth-orbiting satellites generates vast and ever-growing archives of Remote Sensing (RS) images. Natural language presents an intuitive interface for accessing, querying, and interpreting the data from such archives. However, existing Vision-Language Models (VLMs) are predominantly trained on web-scraped, noisy image-text data, exhibiting limited exposure to the specialized domain of RS. This deficiency results in poor performance on RS-specific tasks, as commonly used datasets often lack detailed, scientifically accurate textual descriptions and instead emphasize solely on attributes like date and location. To bridge this critical gap, we introduce GAIA, a novel dataset designed for multi-scale, multi-sensor, and multi-modal RS image analysis. GAIA comprises of 205,150 meticulously curated RS image-text pairs, representing a diverse range of RS modalities associated to different spatial resolutions. Unlike existing vision-language datasets in RS, GAIA specifically focuses on capturing a diverse range of RS applications, providing unique information about environmental changes, natural disasters, and various other dynamic phenomena. The dataset provides a spatially and temporally balanced distribution, spanning across the globe, covering the last 25 years with a balanced temporal distribution of observations. GAIA's construction involved a two-stage process: (1) targeted web-scraping of images and accompanying text from reputable RS-related sources, and (2) generation of five high-quality, scientifically grounded synthetic captions for each image using carefully crafted prompts that leverage the advanced vision-language capabilities of GPT-4o. Our extensive experiments, including fine-tuning of CLIP and BLIP2 models, demonstrate that GAIA significantly improves performance on RS image classification, cross-modal retrieval and image captioning tasks.

Accurate Subseasonal-to-Seasonal (S2S) ocean simulation is critically important for marine research, yet remains challenging due to its substantial thermal inertia and extended time delay. Machine learning (ML)-based models have demonstrated significant advancements in simulation accuracy and computational efficiency compared to traditional numerical methods. Nevertheless, a significant limitation of current ML models for S2S ocean simulation is their inadequate incorporation of physical consistency and the slow-changing properties of the ocean system. In this work, we propose a neural ocean model (NeuralOM) for S2S ocean simulation with a multi-scale interactive graph neural network to emulate diverse physical phenomena associated with ocean systems effectively. Specifically, we propose a multi-stage framework tailored to model the ocean's slowly changing nature. Additionally, we introduce a multi-scale interactive messaging module to capture complex dynamical behaviors, such as gradient changes and multiplicative coupling relationships inherent in ocean dynamics. Extensive experimental evaluations confirm that our proposed NeuralOM outperforms state-of-the-art models in S2S and extreme event simulation. The codes are available at https://github.com/YuanGao-YG/NeuralOM.

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph neural operator approach designed for efficiently solving PDEs on Arbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on https://github.com/lizhihao2022/AMG.

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable operator learning approach with reduced memory requirement and better generalization, called multi-grid tensorized neural operator (MG-TFNO). MG-TFNO scales to large resolutions by leveraging local and global structures of full-scale, real-world phenomena, through a decomposition of both the input domain and the operator's parameter space. Our contributions are threefold: i) we enable parallelization over input samples with a novel multi-grid-based domain decomposition, ii) we represent the parameters of the model in a high-order latent subspace of the Fourier domain, through a global tensor factorization, resulting in an extreme reduction in the number of parameters and improved generalization, and iii) we propose architectural improvements to the backbone FNO. Our approach can be used in any operator learning setting. We demonstrate superior performance on the turbulent Navier-Stokes equations where we achieve less than half the error with over 150x compression. The tensorization combined with the domain decomposition, yields over 150x reduction in the number of parameters and 7x reduction in the domain size without losses in accuracy, while slightly enabling parallelism.

Recent research in speaker recognition aims to address vulnerabilities due to variations between enrolment and test utterances, particularly in the multi-genre phenomenon where the utterances are in different speech genres. Previous resources for Vietnamese speaker recognition are either limited in size or do not focus on genre diversity, leaving studies in multi-genre effects unexplored. This paper introduces VoxVietnam, the first multi-genre dataset for Vietnamese speaker recognition with over 187,000 utterances from 1,406 speakers and an automated pipeline to construct a dataset on a large scale from public sources. Our experiments show the challenges posed by the multi-genre phenomenon to models trained on a single-genre dataset, and demonstrate a significant increase in performance upon incorporating the VoxVietnam into the training process. Our experiments are conducted to study the challenges of the multi-genre phenomenon in speaker recognition and the performance gain when the proposed dataset is used for multi-genre training.

Code-switching (CS) is the alternating use of two or more languages within a conversation or utterance, often influenced by social context and speaker identity. This linguistic phenomenon poses challenges for Automatic Speech Recognition (ASR) systems, which are typically designed for a single language and struggle to handle multilingual inputs. The growing global demand for multilingual applications, including Code-Switching ASR (CSASR), Text-to-Speech (CSTTS), and Cross-Lingual Information Retrieval (CLIR), highlights the inadequacy of existing monolingual datasets. Although some code-switching datasets exist, most are limited to bilingual mixing within homogeneous ethnic groups, leaving a critical need for a large-scale, diverse benchmark akin to ImageNet in computer vision. To bridge this gap, we introduce LinguaMaster, a multi-agent collaboration framework specifically designed for efficient and scalable multilingual data synthesis. Leveraging this framework, we curate SwitchLingua, the first large-scale multilingual and multi-ethnic code-switching dataset, including: (1) 420K CS textual samples across 12 languages, and (2) over 80 hours of audio recordings from 174 speakers representing 18 countries/regions and 63 racial/ethnic backgrounds, based on the textual data. This dataset captures rich linguistic and cultural diversity, offering a foundational resource for advancing multilingual and multicultural research. Furthermore, to address the issue that existing ASR evaluation metrics lack sensitivity to code-switching scenarios, we propose the Semantic-Aware Error Rate (SAER), a novel evaluation metric that incorporates semantic information, providing a more accurate and context-aware assessment of system performance.

Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation method for image classifiers based on the shearlet transform -- a multiscale directional image representation. Current mask explanation methods are regularized by smoothness constraints that protect against undesirable fine-grained explanation artifacts. However, the smoothness of a mask limits its ability to separate fine-detail patterns, that are relevant for the classifier, from nearby nuisance patterns, that do not affect the classifier. ShearletX solves this problem by avoiding smoothness regularization all together, replacing it by shearlet sparsity constraints. The resulting explanations consist of a few edges, textures, and smooth parts of the original image, that are the most relevant for the decision of the classifier. To support our method, we propose a mathematical definition for explanation artifacts and an information theoretic score to evaluate the quality of mask explanations. We demonstrate the superiority of ShearletX over previous mask based explanation methods using these new metrics, and present exemplary situations where separating fine-detail patterns allows explaining phenomena that were not explainable before.