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Computer Vision

Weiquan Wang, Jun Xiao, Chunping Wang, Wei Liu, Zhao Wang, Long Chen

Diffusion models have demonstrated their effectiveness in addressing the inherent uncertainty and indeterminacy in monocular 3D human pose estimation (HPE). Despite their strengths, the need for large search spaces and the corresponding demand for substantial training data make these models prone to generating biomechanically unrealistic poses. This challenge is particularly noticeable in occlusion scenarios, where the complexity of inferring 3D structures from 2D images intensifies. In response to these limitations, we introduce the **Di**screte **Di**ffusion **Pose** (**$\text{Di}^2\text{Pose}$**), a novel framework designed for occluded 3D HPE that capitalizes on the benefits of a discrete diffusion model. Specifically, **$\text{Di}^2\text{Pose}$** employs a two-stage process: it first converts 3D poses into a discrete representation through a pose quantization step, which is subsequently modeled in latent space through a discrete diffusion process. This methodological innovation restrictively confines the search space towards physically viable configurations and enhances the model’s capability to comprehend how occlusions affect human pose within the latent space. Extensive evaluations conducted on various benchmarks (e.g., Human3.6M, 3DPW, and 3DPW-Occ) have demonstrated its effectiveness.

Physical Models · Geoscience

Kun Chen, Peng Ye, Hao Chen, kang chen, Tao Han, Wanli Ouyang, Tao Chen, LEI BAI

Data assimilation is a vital component in modern global medium-range weather forecasting systems to obtain the best estimation of the atmospheric state by combining the short-term forecast and observations. Recently, AI-based data assimilation approaches have attracted increasing attention for their significant advantages over traditional techniques in terms of computational consumption. However, existing AI-based data assimilation methods can only handle observations with a specific resolution, lacking the compatibility and generalization ability to assimilate observations with other resolutions. Considering that complex real-world observations often have different resolutions, we propose the Fourier Neural Processes (FNP) for arbitrary-resolution data assimilation in this paper. Leveraging the efficiency of the designed modules and flexible structure of neural processes, FNP achieves state-of-the-art results in assimilating observations with varying resolutions, and also exhibits increasing advantages over the counterparts as the resolution and the amount of observations increase. Moreover, our FNP trained on a fixed resolution can directly handle the assimilation of observations with out-of-distribution resolutions and the observational information reconstruction task without additional fine-tuning, demonstrating its excellent generalization ability across data resolutions as well as across tasks. Code is available at https://github.com/OpenEarthLab/FNP.

Physical Models · Physics

Nicholas Gao, Stephan Günnemann

Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. Enforcing the permutation antisymmetry of electrons in such generalized neural wave functions remained challenging as existing methods require discrete orbital selection via non-learnable hand-crafted algorithms. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules. We achieve this by relying on Pfaffians rather than Slater determinants. The Pfaffian allows us to enforce the antisymmetry on arbitrary electronic systems without any constraint on electronic spin configurations or molecular structure. Our empirical evaluation finds that a single neural Pfaffian calculates the ground state and ionization energies with chemical accuracy across various systems. On the TinyMol dataset, we outperform the `gold-standard' CCSD(T) CBS reference energies by 1.9m$E_h$ and reduce energy errors compared to previous generalized neural wave functions by up to an order of magnitude.

Physical Models · Physics

Nicholas Gao, Stephan Günnemann

Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. Enforcing the permutation antisymmetry of electrons in such generalized neural wave functions remained challenging as existing methods require discrete orbital selection via non-learnable hand-crafted algorithms. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules. We achieve this by relying on Pfaffians rather than Slater determinants. The Pfaffian allows us to enforce the antisymmetry on arbitrary electronic systems without any constraint on electronic spin configurations or molecular structure. Our empirical evaluation finds that a single neural Pfaffian calculates the ground state and ionization energies with chemical accuracy across various systems. On the TinyMol dataset, we outperform the `gold-standard' CCSD(T) CBS reference energies by 1.9m$E_h$ and reduce energy errors compared to previous generalized neural wave functions by up to an order of magnitude.

Physical Models

Maximilian Herde, Bogdan Raonic, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bezenac, Siddhartha Mishra

We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A novel training strategy leveraging the semi-group property of time-dependent PDEs to allow for significant scaling-up of the training data is also proposed. Poseidon is pretrained on a diverse, large scale dataset for the governing equations of fluid dynamics. It is then evaluated on a suite of 15 challenging downstream tasks that include a wide variety of PDE types and operators. We show that Poseidon exhibits excellent performance across the board by outperforming baselines significantly, both in terms of sample efficiency and accuracy. Poseidon also generalizes very well to new physics that is not seen during pretraining. Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks. Taken together, our results showcase the surprising ability of Poseidon to learn effective representations from a very small set of PDEs during pretraining in order to generalize well to unseen and unrelated PDEs downstream, demonstrating its potential as an effective, general purpose PDE foundation model. Finally, the Poseidon model as well as underlying pretraining and downstream datasets are open sourced, with code being available at https://github.com/camlab-ethz/poseidon and pretrained models and datasets at https://huggingface.co/camlab-ethz.

Physical Models · Climate

Wanghan Xu, Fenghua Ling, zhangwenlong, Tao Han, Hao Chen, Wanli Ouyang, LEI BAI

Data-driven artificial intelligence (AI) models have made significant advancements in weather forecasting, particularly in medium-range and nowcasting. However, most data-driven weather forecasting models are black-box systems that focus on learning data mapping rather than fine-grained physical evolution in the time dimension. Consequently, the limitations in the temporal scale of datasets prevent these models from forecasting at finer time scales. This paper proposes a physics-AI hybrid model (i.e., WeatherGFT) which generalizes weather forecasts to finer-grained temporal scales beyond training dataset. Specifically, we employ a carefully designed PDE kernel to simulate physical evolution on a small time scale (e.g., 300 seconds) and use a parallel neural networks with a learnable router for bias correction. Furthermore, we introduce a lead time-aware training framework to promote the generalization of the model at different lead times. The weight analysis of physics-AI modules indicates that physics conducts major evolution while AI performs corrections adaptively. Extensive experiments show that WeatherGFT trained on an hourly dataset, effectively generalizes forecasts across multiple time scales, including 30-minute, which is even smaller than the dataset's temporal resolution.

Trustworthy Machine Learning

Zhe Tao, Aditya V Thakur

Ensuring that a DNN satisfies a desired property is critical when deploying DNNs in safety-critical applications. There are efficient methods that can verify whether a DNN satisfies a property, as seen in the annual DNN verification competition (VNN-COMP). However, the problem of provably editing a DNN to satisfy a property remains challenging. We present PREPARED, the first efficient technique for provable editing of DNNs. Given a DNN $\mathcal{N}$ with parameters $\theta$, input polytope $P$, and output polytope $Q$, PREPARED finds new parameters $\theta'$ such that $\forall \mathrm{x} \in P . \mathcal{N}(\mathrm{x}; \theta') \in Q$ while minimizing the changes $\lVert{\theta' - \theta}\rVert$. Given a DNN and a property it violates from the VNN-COMP benchmarks, PREPARED is able to provably edit the DNN to satisfy this property within 45 seconds. PREPARED is efficient because it relaxes the NP-hard provable editing problem to solving a linear program. The key contribution is the novel notion of Parametric Linear Relaxation, which enables PREPARED to construct tight output bounds of the DNN that are parameterized by the new parameters $\theta'$. We demonstrate that PREPARED is more efficient and effective compared to prior DNN editing approaches i) using the VNN-COMP benchmarks, ii) by editing CIFAR10 and TinyImageNet image-recognition DNNs, and BERT sentiment-classification DNNs for local robustness, and iii) by training a DNN to model a geodynamics process and satisfy physics constraints.

Physical Models · Physics

Eric Qu, Aditi Krishnapriyan

Scaling has been a critical factor in improving model performance and generalization across various fields of machine learning.It involves how a model’s performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in scaling other types of machine learning models, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations, predicting the energy and forces between atoms in molecules and materials based on atomic configurations. The dominant paradigm in this field is to incorporate numerous physical domain constraints into the model, such as symmetry constraints like rotational equivariance. We contend that these increasingly complex domain constraints inhibit the scaling ability of NNIPs, and such strategies are likely to cause model performance to plateau in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling properties and strategies. Our findings indicate that scaling the model through attention mechanisms is both efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a novel multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations.Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency---at least 10x speed up in inference time, 5x less in memory usage---compared to existing NNIP models. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). After training EScAIP, we test its ability to learn rotational equivariance by predicting forces on new, unseen atomistic systems before and after rotation. The model's force predictions exactly match the rotated forces, suggesting that it has precisely learned rotational equivariance.Finally, we emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept towards developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

Physical Models · Physics

Yifei Zhang, Huan-ang Gao, zhou jiang, Hao Zhao

3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which tracks particles across two consecutive frames. Recently, deep learning-based methods have achieved impressive accuracy in dual-frame fluid motion estimation; however, they heavily depend on large volumes of labeled data. In this paper, we introduce a new method that is **completely self-supervised and notably outperforms its fully-supervised counterparts while requiring only 1\% of the training samples (without labels) used by previous methods.** Our method features a novel zero-divergence loss that is specific to the domain of turbulent flow. Inspired by the success of splat operation in high-dimensional filtering and random fields, we propose a splat-based implementation for this loss which is both efficient and effective. The self-supervised nature of our method naturally supports test-time optimization, leading to the development of a tailored Dynamic Velocimetry Enhancer (DVE) module. We demonstrate that strong cross-domain robustness is achieved through test-time optimization on unseen leave-one-out synthetic domains and real physical/biological domains. Code, data and models are available at [https://github.com/Forrest-110/FluidMotionNet](https://github.com/Forrest-110/FluidMotionNet).

Physical Models · Physics

Yuxuan Ren, Dihan Zheng, Chang Liu, Peiran Jin, Yu Shi, Lin Huang, Jiyan He, Shengjie Luo, Tao Qin, Tie-Yan Liu

In recent years, machine learning has demonstrated impressive capability in handling molecular science tasks. To support various molecular properties at scale, machine learning models are trained in the multi-task learning paradigm. Nevertheless, data of different molecular properties are often not aligned: some quantities, e.g. equilibrium structure, demand more cost to compute than others, e.g. energy, so their data are often generated by cheaper computational methods at the cost of lower accuracy, which cannot be directly overcome through multi-task learning. Moreover, it is not straightforward to leverage abundant data of other tasks to benefit a particular task. To handle such data heterogeneity challenges, we exploit the specialty of molecular tasks that there are physical laws connecting them, and design consistency training approaches that allow different tasks to exchange information directly so as to improve one another. Particularly, we demonstrate that the more accurate energy data can improve the accuracy of structure prediction. We also find that consistency training can directly leverage force and off-equilibrium structure data to improve structure prediction, demonstrating a broad capability for integrating heterogeneous data.

Physical Models · Climate

Prakhar Srivastava, Ruihan Yang, Gavin Kerrigan, Gideon Dresdner, Jeremy McGibbon, Christopher S. Bretherton, Stephan Mandt

In climate science and meteorology, high-resolution local precipitation (rain and snowfall) predictions are limited by the computational costs of simulation-based methods. Statistical downscaling, or super-resolution, is a common workaround where a low-resolution prediction is improved using statistical approaches. Unlike traditional computer vision tasks, weather and climate applications require capturing the accurate conditional distribution of high-resolution given low-resolution patterns to assure reliable ensemble averages and unbiased estimates of extreme events, such as heavy rain. This work extends recent video diffusion models to precipitation super-resolution, employing a deterministic downscaler followed by a temporally-conditioned diffusion model to capture noise characteristics and high-frequency patterns. We test our approach on FV3GFS output, an established large-scale global atmosphere model, and compare it against six state-of-the-art baselines. Our analysis, capturing CRPS, MSE, precipitation distributions, and qualitative aspects using California and the Himalayas as examples, establishes our method as a new standard for data-driven precipitation downscaling.

Physical Models · Climate

Chiu-Wai Yan, Shi Quan Foo, Van Hoan Trinh, Dit-Yan Yeung, Ka-Hing Wong, Wai-kin Wong

Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information. The two loss terms work together to replace the traditional L2 losses such as MSE and weighted MSE for the spatiotemporal prediction problem on signal-based data. Our method is generic, parameter-free and efficient. Extensive experiments using one synthetic dataset and three radar echo datasets demonstrate that our method improves perceptual metrics and meteorology skill scores, with a small trade-off to pixel-wise accuracy and structural similarity. Moreover, to improve the error margin in meteorological skill scores such as Critical Success Index (CSI) and Fractions Skill Score (FSS), we propose and adopt the Regional Histogram Divergence (RHD), a distance metric that considers the patch-wise similarity between signal-based imagery patterns with tolerance to local transforms.

Computer Vision

Ye Fang, Zeyi Sun, Tong Wu, Jiaqi Wang, Ziwei Liu, Gordon Wetzstein, Dahua Lin

Physically realistic materials are pivotal in augmenting the realism of 3D assets across various applications and lighting conditions. However, existing 3D assets and generative models often lack authentic material properties. Manual assignment of materials using graphic software is a tedious and time-consuming task. In this paper, we exploit advancements in Multimodal Large Language Models (MLLMs), particularly GPT-4V, to present a novel approach, Make-it-Real: 1) We demonstrate that GPT-4V can effectively recognize and describe materials, allowing the construction of a detailed material library. 2) Utilizing a combination of visual cues and hierarchical text prompts, GPT-4V precisely identifies and aligns materials with the corresponding components of 3D objects. 3) The correctly matched materials are then meticulously applied as reference for the new SVBRDF material generation according to the original albedo map, significantly enhancing their visual authenticity. Make-it-Real offers a streamlined integration into the 3D content creation workflow, showcasing its utility as an essential tool for developers of 3D assets.

Physical Models · Physics

YIDI SHAO, Chen Change Loy, Bo Dai

Garment animation is ubiquitous in various applications, such as virtual reality, gaming, and film producing. Recently, learning-based approaches obtain compelling performance in animating diverse garments under versatile scenarios. Nevertheless, to mimic the deformations of the observed garments, data-driven methods require large scale of garment data, which are both resource-wise expensive and time-consuming. In addition, forcing models to match the dynamics of observed garment animation may hinder the potentials to generalize to unseen cases. In this paper, instead of using garment-wise supervised-learning we adopt a disentangled scheme to learn how to animate observed garments: 1). learning constitutive behaviors from the observed cloth; 2). dynamically animate various garments constrained by the learned constitutive laws. Specifically, we propose Energy Unit network (EUNet) to model the constitutive relations in the format of energy. Without the priors from analytical physics models and differentiable simulation engines, EUNet is able to directly capture the constitutive behaviors from the observed piece of cloth and uniformly describes the change of energy caused by deformations, such as stretching and bending. We further apply the pre-trained EUNet to animate various garments based on energy optimizations. The disentangled scheme alleviates the need of garment data and enables us to utilize the dynamics of a piece of cloth for animating garments. Experiments show that while EUNet effectively delivers the energy gradients due to the deformations, models constrained by EUNet achieve more stable and physically plausible performance comparing with those trained in garment-wise supervised manner.

Physical Models · Climate

Salva Rühling Cachay, Brian Henn, Oliver Watt-Meyer, Christopher S. Bretherton, Rose Yu

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS.Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines.The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill.This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies. Code is available at [https://github.com/Rose-STL-Lab/spherical-dyffusion](https://github.com/Rose-STL-Lab/spherical-dyffusion).

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Samuel Holt, Zhaozhi Qian, Tennison Liu, Jim Weatherall, Mihaela van der Schaar

The discovery of dynamical systems is crucial across a range of fields, including pharmacology, epidemiology, and physical sciences. *Accurate* and *interpretable* modeling of these systems is essential for understanding complex temporal processes, optimizing interventions, and minimizing adverse effects. In pharmacology, for example, precise modeling of drug dynamics is vital to maximize therapeutic efficacy while minimizing patient harm, as in chemotherapy. However, current models, often developed by human experts, are limited by high cost, lack of scalability, and restriction to existing human knowledge. In this paper, we present the **Data-Driven Discovery (D3)** framework, a novel approach leveraging Large Language Models (LLMs) to iteratively discover and refine interpretable models of dynamical systems, demonstrated here with pharmacological applications. Unlike traditional methods, D3 enables the LLM to propose, acquire, and integrate new features, validate, and compare dynamical systems models, uncovering new insights into pharmacokinetics. Experiments on a pharmacokinetic Warfarin dataset reveal that D3 identifies a new plausible model that is well-fitting, highlighting its potential for precision dosing in clinical applications.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

William Redman, Juan Bello-Rivas, Maria Fonoberova, Ryan Mohr, Yannis Kevrekidis, Igor Mezic

Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding of these phenomena has the potential to advance improvements in training efficiency and robustness, the lack of methods for identifying when DNN models have equivalent dynamics limits the insight that can be gained from prior work. Topological conjugacy, a notion from dynamical systems theory, provides a precise definition of dynamical equivalence, offering a possible route to address this need. However, topological conjugacies have historically been challenging to compute. By leveraging advances in Koopman operator theory, we develop a framework for identifying conjugate and non-conjugate training dynamics. To validate our approach, we demonstrate that comparing Koopman eigenvalues can correctly identify a known equivalence between online mirror descent and online gradient descent. We then utilize our approach to: (a) identify non-conjugate training dynamics between shallow and wide fully connected neural networks; (b) characterize the early phase of training dynamics in convolutional neural networks; (c) uncover non-conjugate training dynamics in Transformers that do and do not undergo grokking. Our results, across a range of DNN architectures, illustrate the flexibility of our framework and highlight its potential for shedding new light on training dynamics.

Robotics

Yanjiang Guo, Yucheng Hu, Jianke Zhang, Yen-Jen Wang, Xiaoyu Chen, Chaochao Lu, Jianyu Chen

Diffusion models have demonstrated remarkable capabilities in image generation tasks, including image editing and video creation, representing a good understanding of the physical world. On the other line, diffusion models have also shown promise in robotic control tasks by denoising actions, known as diffusion policy. Although the diffusion generative model and diffusion policy exhibit distinct capabilities—image prediction and robotic action, respectively—they technically follow similar denoising process. In robotic tasks, the ability to predict future images and generate actions is highly correlated since they share the same underlying dynamics of the physical world. Building on this insight, we introduce \textbf{PAD}, a novel visual policy learning framework that unifies image \textbf{P}rediction and robot \textbf{A}ction within a joint \textbf{D}enoising process. Specifically, PAD utilizes Diffusion Transformers (DiT) to seamlessly integrate images and robot states, enabling the simultaneous prediction of future images and robot actions. Additionally, PAD supports co-training on both robotic demonstrations and large-scale video datasets and can be easily extended to other robotic modalities, such as depth images. PAD outperforms previous methods, achieving a significant 38.9\% relative improvement on the full Metaworld benchmark, by utilizing a single text-conditioned visual policy within a data-efficient imitation learning setting. Furthermore, PAD demonstrates superior generalization to unseen tasks in real-world robot manipulation settings with 28.0\% success rate increase compared to the strongest baseline. Videos of PAD can be found at https://sites.google.com/view/pad-paper

Deep Learning · Robustness

ZAITANG LI, Pin-Yu Chen, Tsung-Yi Ho

Current studies on adversarial robustness mainly focus on aggregating \textit{local} robustness results from a set of data samples to evaluate and rank different models. However, the local statistics may not well represent the true \textit{global} robustness of the underlying unknown data distribution. To address this challenge, this paper makes the first attempt to present a new framework, called \textit{GREAT Score}, for global robustness evaluation of adversarial perturbation using generative models. Formally, GREAT Score carries the physical meaning of a global statistic capturing a mean certified attack-proof perturbation level over all samples drawn from a generative model. For finite-sample evaluation, we also derive a probabilistic guarantee on the sample complexity and the difference between the sample mean and the true mean. GREAT Score has several advantages: (1) Robustness evaluations using GREAT Score are efficient and scalable to large models, by sparing the need of running adversarial attacks. In particular, we show high correlation and significantly reduced computation cost of GREAT Score when compared to the attack-based model ranking on RobustBench \cite{croce2021robustbench}. (2) The use of generative models facilitates the approximation of the unknown data distribution. In our ablation study with different generative adversarial networks (GANs), we observe consistency between global robustness evaluation and the quality of GANs. (3) GREAT Score can be used for remote auditing of privacy-sensitive black-box models, as demonstrated by our robustness evaluation on several online facial recognition services.

Physical Models · Physics

Jiahe Huang, Guandao Yang, Zichen Wang, Jeong Joon Park

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical solvers. Most existing forward or inverse PDE approaches perform poorly when the observations on the data or the underlying coefficients are incomplete, which is a common assumption for real-world measurements. In this work, we propose DiffusionPDE that can simultaneously fill in the missing information and solve a PDE by modeling the joint distribution of the solution and coefficient spaces. We show that the learned generative priors lead to a versatile framework for accurately solving a wide range of PDEs under partial observation, significantly outperforming the state-of-the-art methods for both forward and inverse directions.