Neural simulators for modeling complex dynamical systems have been extensively studied for various real-world applications, such as weather forecasting, ocean current prediction, and computational fluid dynamics simulation. Although they have demonstrated powerful fitting and predicting, most existing models are only built to learn single-system dynamics. Several advanced researches have considered learning dynamics across environments, which can exploit the potential commonalities among the dynamics across environments and adapt to new environments. However, these methods still are prone to scarcity problems where per-environment data is sparse or limited. Therefore, we propose a novel CoNDP (Context-Informed Neural ODE Processes) to achieve learning system dynamics from sparse observations across environments. It can fully use contextual information of each environment to better capture the intrinsic commonalities across environments and distinguishable differences among environments while modeling uncertainty of system evolution, producing more accurate predictions. Intensive experiments are conducted on five complex dynamical systems in various fields. Results show that the proposed CoNDP can achieve optimal results compared with common neural simulators and state-of-the-art cross-environmental models.
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Vertical Symbolic Regression (VSR) has recently been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by building from reduced-form equations involving a subset of variables to all variables. While deep neural networks have shown promise in enhancing symbolic regression, directly integrating VSR with deep networks faces challenges such as gradient propagation and engineering complexities due to the tree representation of expressions. We propose Vertical Symbolic Regression using Deep Policy Gradient (VSR-DPG) and demonstrate that VSR-DPG can recover ground-truth equations involving multiple input variables, significantly beyond both deep reinforcement learning-based approaches and previous VSR variants. Our VSR-DPG models symbolic regression as a sequential decision-making process, in which equations are built from repeated applications of grammar rules. The integrated deep model is trained to maximize a policy gradient objective. Experimental results demonstrate that our VSR-DPG significantly outperforms popular baselines in identifying both algebraic equations and ordinary differential equations on a series of benchmarks.
Geometry-Guided Conditional Adaptation for Surrogate Models of Large-Scale 3D PDEs on Arbitrary Geometries
PDF ↗Deep learning surrogate models aim to accelerate the solving of partial differential equations (PDEs) and have achieved certain promising results. Although several main-stream models through neural operator learning have been applied to delve into PDEs on varying geometries, they were designed to map the complex geometry to a latent uniform grid, which is still challenging to learn by the networks with general architectures. In this work, we rethink the critical factors of PDE solutions and propose a novel model-agnostic framework, called 3D Geometry-Guided Conditional adaptation (3D-GeoCA), for solving PDEs on arbitrary 3D geometries. Starting with a 3D point cloud geometry encoder, 3D-GeoCA can extract the essential and robust representations of any kind of geometric shapes, which conditionally guides the adaptation of hidden features in the surrogate model. We conduct experiments on two public computational fluid dynamics datasets, the Shape-Net Car and Ahmed-Body dataset, using several surrogate models as the backbones with various point cloud geometry encoders to simulate corresponding large-scale Reynolds Average Navier-Stokes equations. Equipped with 3D-GeoCA, these backbone models can reduce the L-2 error by a large margin. Moreover, this 3D-GeoCA is model-agnostic so that it can be applied to any surrogate model.
We propose a meta-learning method for modeling Hamiltonian dynamics from a limited number of data. Although Hamiltonian neural networks have been successfully used for modeling dynamics that obey the energy conservation law, they require many data to achieve high performance. The proposed method meta-learns our neural network-based model using datasets in various dynamical systems, such that our model can predict vector fields of unseen systems. In our model, a system representation is inferred from given small data using an encoder network. Then, the system-specific vector field is predicted by modeling the Hamiltonian using a Gaussian process (GP) with neural network-based mean and kernel functions that depend on the inferred system representation. This GP-based Hamiltonian allows us to analytically obtain predictions that are adapted to small data while imposing the constraint of the conservation law. The neural networks are shared across systems, which enables us to learn knowledge from multiple systems, and use it for unseen systems. In our experiments, we demonstrate that the proposed method outperforms existing methods for predicting dynamics from a small number of observations in target systems.
Negative-Binomial Randomized Gamma Dynamical Systems for Heterogeneous Overdispersed Count Time Sequences
PDF ↗Modeling count-valued time sequences has been receiving growing interests because count time sequences naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.
Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be established. This limitation could be a potential reason why the learning process for PINNs is not always efficient and the numerical results may suggest nonphysical behavior. Besides, there is little research on their applications on downstream tasks. To address these issues, we propose structure-preserving PINNs to improve their performance and broaden their applications for downstream tasks. Firstly, by leveraging prior knowledge about the physical system, a structure‐preserving loss function is designed to assist the PINN in learning the underlying structure. Secondly, a framework that utilizes structure-preserving PINN for robust image recognition is proposed. Here, preserving the Lyapunov structure of the underlying system ensures the stability of the system. Experimental results demonstrate that the proposed method improves the numerical accuracy of PINNs for partial differential equations (PDEs). Furthermore, the robustness of the model against adversarial perturbations in image data is enhanced.
FlagVNE: A Flexible and Generalizable Reinforcement Learning Framework for Network Resource Allocation
PDF ↗Virtual network embedding (VNE) is an essential resource allocation task in network virtualization, aiming to map virtual network requests (VNRs) onto physical infrastructure. Reinforcement learning (RL) has recently emerged as a promising solution to this problem. However, existing RL-based VNE methods are limited by the unidirectional action design and one-size-fits-all training strategy, resulting in restricted searchability and generalizability. In this paper, we propose a flexible and generalizable RL framework for VNE, named FlagVNE. Specifically, we design a bidirectional action-based Markov decision process model that enables the joint selection of virtual and physical nodes, thus improving the exploration flexibility of solution space. To tackle the expansive and dynamic action space, we design a hierarchical decoder to generate adaptive action probability distributions and ensure high training efficiency. Furthermore, to overcome the generalization issue for varying VNR sizes, we propose a meta-RL-based training method with a curriculum scheduling strategy, facilitating specialized policy training for each VNR size. Finally, extensive experimental results show the effectiveness of FlagVNE across multiple key metrics. Our code is available at https://github.com/GeminiLight/flag-vne.
Self-Supervised Monocular Depth Estimation in the Dark: Towards Data Distribution Compensation
PDF ↗Nighttime self-supervised monocular depth estimation has received increasing attention in recent years. However, using night images for self-supervision is unreliable because the photometric consistency assumption is usually violated in the videos taken under complex lighting conditions. Even with domain adaptation or photometric loss repair, performance is still limited by the poor supervision of night images on trainable networks. In this paper, we propose a self-supervised nighttime monocular depth estimation method that does not use any night images during training. Our framework utilizes day images as a stable source for self-supervision and applies physical priors (e.g., wave optics, reflection model and read-shot noise model) to compensate for some key day-night differences. With day-to-night data distribution compensation, our framework can be trained in an efficient one-stage self-supervised manner. Though no nighttime images are considered during training, qualitative and quantitative results demonstrate that our method achieves SoTA depth estimating results on the challenging nuScenes-Night and RobotCar-Night compared with existing methods.
Accurate and timely mapping of flood extent from high resolution satellite imagery plays a crucial role in disaster management such as damage assessment and relief activities. However, current state-of-the-art solutions are based on U-Net, which cannot segment the flood pixels accurately due to the ambiguous pixels (e.g., tree canopies, clouds) that prevent a direct judgement from only the spectral features. Thanks to the digital elevation model (DEM) data readily available from sources such as United States Geological Survey (USGS), this work explores the use of an elevation map to improve flood extent mapping. We propose, EvaNet, an elevation-guided segmentation model based on the encoder-decoder architecture with two novel techniques: (1) a loss function encoding the physical law of gravity that if a location is flooded (resp. dry), then its adjacent locations with a lower (resp. higher) elevation must also be flooded (resp. dry); (2) a new (de)convolution operation that integrates the elevation map by a location-sensitive gating mechanism to regulate how much spectral features flow through adjacent layers. Extensive experiments show that EvaNet significantly outperforms the U-Net baselines, and works as a perfect drop-in replacement for U-Net in existing solutions to flood extent mapping. EvaNet is open-sourced at https://github.com/MTSami/EvaNet.
Face Recognition (FR) systems can suffer from physical (i.e., print photo) and digital (i.e., DeepFake) attacks. However, previous related work rarely considers both situations at the same time. This implies the deployment of multiple models and thus more computational burden. The main reasons for this lack of an integrated model are caused by two factors: (1) The lack of a dataset including both physical and digital attacks which the same ID covers the real face and all attack types; (2) Given the large intra-class variance between these two attacks, it is difficult to learn a compact feature space to detect both attacks simultaneously. To address these issues, we collect a Unified physical-digital Attack dataset, called UniAttackData. The dataset consists of 1,800 participations of 2 and 12 physical and digital attacks, respectively, resulting in a total of 28,706 videos. Then, we propose a Unified Attack Detection framework based on Vision-Language Models (VLMs), namely UniAttackDetection, which includes three main modules: the Teacher-Student Prompts (TSP) module, focused on acquiring unified and specific knowledge respectively; the Unified Knowledge Mining (UKM) module, designed to capture a comprehensive feature space; and the Sample-Level Prompt Interaction (SLPI) module, aimed at grasping sample-level semantics. These three modules seamlessly form a robust unified attack detection framework. Extensive experiments on UniAttackData and three other datasets demonstrate the superiority of our approach for unified face attack detection. Dataset link: https://sites.google.com/view/face-anti-spoofing-challenge/dataset-download/uniattackdatacvpr2024
End-to-End Phase Field Model Discovery Combining Experimentation, Crowdsourcing, Simulation and Learning
PDF ↗The availability of tera-byte scale experiment data calls for AI driven approaches which automatically discover scientific models from data. Nonetheless, significant challenges present in AI-driven scientific discovery: (i) The annotation of large scale datasets requires fundamental re-thinking in developing scalable crowdsourcing tools. (ii) The learning of scientific models from data calls for innovations beyond black-box neural nets. (iii) Novel visualization & diagnosis tools are needed for the collaboration of experimental and theoretical physicists, and computer scientists. We present Phase-Field-Lab platform for end-to-end phase field model discovery, which automatically discovers phase field physics models from experiment data, integrating experimentation, crowdsourcing, simulation and learning. Phase-Field-Lab combines (i) a streamlined annotation tool which reduces the annotation time (by ~50-75%), while increasing annotation accuracy compared to baseline; (ii) an end-to-end neural model which automatically learns phase field models from data by embedding phase field simulation and existing domain knowledge into learning; and (iii) novel interfaces and visualizations to integrate our platform into the scientific discovery cycle of domain scientists. Our platform is deployed in the analysis of nano-structure evolution in materials under extreme conditions (high temperature and irradiation). Our approach reveals new properties of nano-void defects, which otherwise cannot be detected via manual analysis.
Accurate Parameter Estimation for Safety-Critical Systems with Unmodeled Dynamics (Abstract Reprint)
PDF ↗Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a Õ(√t) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.
Planning is the act of deliberative thinking before acting. It is based on a symbolic model of the world and the options to act in it, usually defined in function-free first-order logic. The task is to find a sequence of actions (a plan) that leads from a given current state to a desired goal state. The basic, purely physical description may be augmented with a partially ordered grammar-like structure (a Hierarchical Task Network or HTN), which can describe expert knowledge, or practical, legal, or operational requirements. In this talk, I will survey a variety of methods for automatically deriving plans using symbolic methods for planning -- from both my past and future research. These symbolic methods -- in some sense -- translate planning problems into other, simpler symbolic representations and reason over them to find plans. As a basis for these methods, I will firstly introduce relevant theoretical results on planning. First, I will discuss the expressive power of planning formalisms (ECAI'14, ICAPS'16) and second, the computational complexity of HTN planning and related tasks such as HTN plan verification, plan modification, and plan recognition (ICAPS'15, ICAPS'16). Based on these theoretical results, I will develop why SAT-based HTN planning is possible and how it can be implemented. To this end, I will survey several of my publications at top-tier conferences, including papers at ICAPS'17, AAAI'18, AAAI'19, IJCAI'19, AAAI'20, and ICAPS'21 -- in which I developed an highly SAT-based planner for HTN problems including the ability to find optimal plans as well as the grounding as a preprocessing step. Here I will also give an outlook on future developments and new ideas that I propose for SAT-based planning -- including the exploitation of structures in plan (e.g.\ landmarks or operator-counting constraints). Next, I will present the idea of expressing lifted classical planning as SAT (ICAPS'22). The resulting planner LiSAT was the first lifted SAT-based planner -- and proved highly efficient and outperformed all other lifted planners at the time of publication. Notably, LiSAT was the first planner (lifted or grounded) and still is the only one to solve the challenging OrganicSynthesis benchmark -- and could even prove optimality for all plans. I will also outline future ideas to further improve the efficiency of LiSAT. Lastly, I introduce the notion of planning with symbolic symbolic representations (AAAI'21 and ICAPS'23). Here one uses Binary Decision Diagrams to encode large sets of states efficiently. For expressing the additional structure encoded by HTNs, I show how BDDs can be suitably integrated into finite automata. Based on this representation, an efficient and optimal planning algorithm can be derived. Additionally, I show how this algorithm can be extended to also cover oversubscription planning.
Flood mapping on Earth imagery is crucial for disaster management, but its efficacy is hampered by the lack of high-quality training labels. Given high-resolution Earth imagery with coarse and noisy training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the true high-resolution labels while training neural network parameters. Traditional methods are largely based on specific physical properties and thus fall short of capturing the rich domain constraints expressed by symbolic logic. Neural-symbolic models can capture rich domain knowledge, but existing methods do not address the unique spatial challenges inherent in flood mapping on high-resolution imagery. To fill this gap, we propose a spatial-logic-aware weakly supervised learning framework. Our framework integrates symbolic spatial logic inference into probabilistic learning in a weakly supervised setting. To reduce the time costs of logic inference on vast high-resolution pixels, we propose a multi-resolution spatial reasoning algorithm to infer true labels while training neural network parameters. Evaluations of real-world flood datasets show that our model outperforms several baselines in prediction accuracy. The code is available at https://github.com/spatialdatasciencegroup/SLWSL.
Fairness-awareness has emerged as an essential building block for the responsible use of artificial intelligence in real applications. In many cases, inequity in performance is due to the change in distribution over different regions. While techniques have been developed to improve the transferability of fairness, a solution to the problem is not always feasible with no samples from the new regions, which is a bottleneck for pure data-driven attempts. Fortunately, physics-based mechanistic models have been studied for many problems with major social impacts. We propose SimFair, a physics-guided fairness-aware learning framework, which bridges the data limitation by integrating physical-rule-based simulation and inverse modeling into the training design. Using temperature prediction as an example, we demonstrate the effectiveness of the proposed SimFair in fairness preservation.
Urban transformations have profound societal impact on both individuals and communities at large. Accurately assessing these shifts is essential for understanding their underlying causes and ensuring sustainable urban planning. Traditional measurements often encounter constraints in spatial and temporal granularity, failing to capture real-time physical changes. While street view imagery, capturing the heartbeat of urban spaces in a pedestrian point of view, can add as a high-definition, up-to-date, and on-the-ground visual proxy of urban change. We curate the largest street view time series dataset to date, and propose an end-to-end change detection model to effectively capture physical alterations in the built environment at scale. We demonstrate the effectiveness of our proposed method by benchmark comparisons with previous literature and implementing it at the city-wide level. Our approach has the potential to supplement existing dataset and serve as a fine-grained and accurate assessment of urban change.
Sea-level rise is a well-known consequence of climate change. Several studies have estimated the social and economic impact of the increase in extreme flooding. An efficient way to mitigate its consequences is the development of a flood alert and prediction system, based on high-resolution numerical models and robust sensing networks. However, current models use various simplifying assumptions that compromise accuracy to ensure solvability within a reasonable timeframe, hindering more regular and cost-effective forecasts for various locations along the shoreline. To address these issues, this work proposes a hybrid model for multimodal data processing that combines physics-based numerical simulations, data obtained from a network of sensors, and satellite images to provide refined wave and sea-surface height forecasts, with real results obtained in a critical location within the Port of Santos (the largest port in Latin America). Our approach exhibits faster convergence than data-driven models while achieving more accurate predictions. Moreover, the model handles irregularly sampled time series and missing data without the need for complex preprocessing mechanisms or data imputation while keeping low computational costs through a combination of time encoding, recurrent and graph neural networks. Enabling raw sensor data to be easily combined with existing physics-based models opens up new possibilities for accurate extreme storm tide events forecast systems that enhance community safety and aid policymakers in their decision-making processes.
Global Climate Models (GCMs) simulate low resolution climate projections on a global scale. The native resolution of GCMs is generally too low for societal-level decision-making. To enhance the spatial resolution, downscaling is often applied to GCM output. Statistical downscaling techniques, in particular, are well-established as a cost-effective approach. They require significantly less computational time than physics-based dynamical downscaling. In recent years, deep learning has gained prominence in statistical downscaling, demonstrating significantly lower error rates compared to traditional statistical methods. However, a drawback of regression-based deep learning techniques is their tendency to overfit to the mean sample intensity. Extreme values as a result are often underestimated. Problematically, extreme events have the largest societal impact. We propose Quantile-Regression-Ensemble (QRE), an innovative deep learning algorithm inspired by boosting methods. Its primary objective is to avoid trade-offs between fitting to sample means and extreme values by training independent models on a partitioned dataset. Our QRE is robust to redundant models and not susceptible to explosive ensemble weights, ensuring a reliable training process. QRE achieves lower Mean Squared Error (MSE) compared to various baseline models. In particular, our algorithm has a lower error for high-intensity precipitation events over New Zealand, highlighting the ability to represent extreme events accurately.
Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools for WDS play a crucial role in reaching UN's sustainable developmental goal (SDG) 6 - "Clean water and sanitation for all". In this realm, we propose a novel and efficient machine learning emulator, more precisely, a physics-informed deep learning (DL) model, for hydraulic state estimation in WDS. Using a recursive approach, our model only needs a few graph convolutional neural network (GCN) layers and employs an innovative algorithm based on message passing. Unlike conventional machine learning tasks, the model uses hydraulic principles to infer two additional hydraulic state features in the process of reconstructing the available ground truth feature in an unsupervised manner. To the best of our knowledge, this is the first DL approach to emulate the popular hydraulic simulator EPANET, utilizing no additional information. Like most DL models and unlike the hydraulic simulator, our model demonstrates vastly faster emulation times that do not increase drastically with the size of the WDS. Moreover, we achieve high accuracy on the ground truth and very similar results compared to the hydraulic simulator as demonstrated through experiments on five real-world WDS datasets.
Efficiently modeling spatio-temporal (ST) physical processes and observations presents a challenging problem for the deep learning community. Many recent studies have concentrated on meticulously reconciling various advantages, leading to designed models that are neither simple nor practical. To address this issue, this paper presents a systematic study on existing shortcomings faced by off-the-shelf models, including lack of local fidelity, poor prediction performance over long time-steps, low scalability, and inefficiency. To systematically address the aforementioned problems, we propose an EarthFarseer, a concise framework that combines parallel local convolutions and global Fourier-based transformer architectures, enabling dynamically capture the local-global spatial interactions and dependencies. EarthFarseer also incorporates a multi-scale fully convolutional and Fourier architectures to efficiently and effectively capture the temporal evolution. Our proposal demonstrates strong adaptability across various tasks and datasets, with fast convergence and better local fidelity in long time-steps predictions. Extensive experiments and visualizations over eight human society physical and natural physical datasets demonstrates the state-of-the-art performance of EarthFarseer. We release our code at https://github.com/easylearningscores/EarthFarseer.