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Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable training. These challenges arise particularly from the ill-conditioning of the optimization problem, caused by the differential terms in the loss function. To address these issues, we propose learning a solver, i.e., solving PDEs using a physics-informed iterative algorithm trained on data. Our method learns to condition a gradient descent algorithm that automatically adapts to each PDE instance, significantly accelerating and stabilizing the optimization process and enabling faster convergence of physics-aware models. Furthermore, while traditional physics-informed methods solve for a single PDE instance, our approach addresses parametric PDEs. Specifically, our method integrates the physical loss gradient with the PDE parameters to solve over a distribution of PDE parameters, including coefficients, initial conditions, or boundary conditions. We demonstrate the effectiveness of our method through empirical experiments on multiple datasets, comparing training and test-time optimization performance.

Long document summarization poses a significant challenge in natural language processing due to input lengths that exceed the capacity of most state-of-the-art pre-trained language models. This study proposes a hierarchical framework that segments and condenses information from long documents, subsequently fine-tuning the processed text with an abstractive summarization model. Unsupervised topic segmentation methods identify semantically appropriate breakpoints. The condensation stage utilizes an unsupervised generation model to generate condensed data, and our current experiments employ ChatGPT(v3.5). The summarization stage fine-tunes the abstractive summarization model on the condensed data to generate the final results. This framework enables long documents to be processed on models even when the document length exceeds the model's maximum input size. The exclusion of the entire document from the summarization model reduces the time and computational resources required for training, making the framework suitable for contexts with constrained local computational resources.

Machine learning based autonomous driving systems often face challenges with safety-critical scenarios that are rare in real-world data, hindering their large-scale deployment. While increasing real-world training data coverage could address this issue, it is costly and dangerous. This work explores generating safety-critical driving scenarios by modifying complex real-world regular scenarios through trajectory optimization. We propose ReGentS, which stabilizes generated trajectories and introduces heuristics to avoid obvious collisions and optimization problems. Our approach addresses unrealistic diverging trajectories and unavoidable collision scenarios that are not useful for training robust planner. We also extend the scenario generation framework to handle real-world data with up to 32 agents. Additionally, by using a differentiable simulator, our approach simplifies gradient descent-based optimization involving a simulator, paving the way for future advancements. The code is available at https://github.com/valeoai/ReGentS., Comment: Accepted to ECCV 2024 W-CODA Workshop

In this study, we introduce a novel approach aimed at addressing the longstanding baryon-anti-baryon asymmetry conundrum. Our proposed mechanism suggests that baryon numbers were generated during the inflationary epoch through the dynamics of the inflaton field coupled with an explicit baryon number violating interaction. Notably, during inflation, it is possible to halt the baryon number generation process via a symmetry restoration phase transition. We elucidate that prior to this phase transition, baryon numbers could be synthesized and preserved within classical field configurations. Subsequently, following the phase transition, these baryon numbers were liberated as particles. Crucially, we demonstrate that this mechanism of baryon number production is intricately linked with significant cosmological collider signals and gravitational wave (GW) signals, offering a compelling framework to explore the origins of the universe's matter-antimatter asymmetry.

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In cases where small numbers or noise play a crucial role, these differential equations are replaced with memoryless Markovian models, where discrete individuals can be members of a compartment and transition stochastically. Classic stochastic simulation algorithms, such as Gillespie's algorithm and the next reaction method, can be employed to solve these Markovian models exactly. The intricate coupling between models at different scales underscores the importance of multiscale modelling in infectious diseases. However, several computational challenges arise when the multiscale model becomes non-Markovian. In this paper, we address these challenges by developing a novel exact stochastic simulation algorithm. We apply it to a showcase multiscale system where all individuals share the same deterministic within-host model while the population-level dynamics are governed by a stochastic formulation. We demonstrate that as long as the within-host information is harvested at a reasonable resolution, the novel algorithm we develop will always be accurate. Moreover, the novel algorithm we develop is general and can be easily applied to other multiscale models in (or outside) the realm of infectious diseases., Comment: 23 pages, 7 figures

Web-scale search systems typically tackle the scalability challenge with a two-step paradigm: retrieval and ranking. The retrieval step, also known as candidate selection, often involves extracting standardized entities, creating an inverted index, and performing term matching for retrieval. Such traditional methods require manual and time-consuming development of query models. In this paper, we discuss applying learning-to-retrieve technology to enhance LinkedIns job search and recommendation systems. In the realm of promoted jobs, the key objective is to improve the quality of applicants, thereby delivering value to recruiter customers. To achieve this, we leverage confirmed hire data to construct a graph that evaluates a seeker's qualification for a job, and utilize learned links for retrieval. Our learned model is easy to explain, debug, and adjust. On the other hand, the focus for organic jobs is to optimize seeker engagement. We accomplished this by training embeddings for personalized retrieval, fortified by a set of rules derived from the categorization of member feedback. In addition to a solution based on a conventional inverted index, we developed an on-GPU solution capable of supporting both KNN and term matching efficiently.

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies., Comment: 60 pages, 6 figures

Point-level supervised temporal action localization (PTAL) aims at recognizing and localizing actions in untrimmed videos where only a single point (frame) within every action instance is annotated in training data. Without temporal annotations, most previous works adopt the multiple instance learning (MIL) framework, where the input video is segmented into non-overlapped short snippets, and action classification is performed independently on every short snippet. We argue that the MIL framework is suboptimal for PTAL because it operates on separated short snippets that contain limited temporal information. Therefore, the classifier only focuses on several easy-to-distinguish snippets instead of discovering the whole action instance without missing any relevant snippets. To alleviate this problem, we propose a novel method that localizes actions by generating and evaluating action proposals of flexible duration that involve more comprehensive temporal information. Moreover, we introduce an efficient clustering algorithm to efficiently generate dense pseudo labels that provide stronger supervision, and a fine-grained contrastive loss to further refine the quality of pseudo labels. Experiments show that our proposed method achieves competitive or superior performance to the state-of-the-art methods and some fully-supervised methods on four benchmarks: ActivityNet 1.3, THUMOS 14, GTEA, and BEOID datasets., Comment: BMVC 2023

We investigate the cosmological collider (CC) signal arising from the tree-level exchange of a scalar spectator particle with a non-Bunch Davies (BD) initial state. We decompose the inflaton correlators into seed integrals, which we compute analytically by solving the bootstrap equations. We show that the non-BD initial state eliminates the Hubble scale Boltzmann suppression $e^{-\pi m /H}$ that usually affects the CC signal. Consequently, in this scenario, the CC can probe an energy scale much higher than the inflationary Hubble scale $H$.

For numerical design, the development of efficient and accurate surrogate models is paramount. They allow us to approximate complex physical phenomena, thereby reducing the computational burden of direct numerical simulations. We propose INFINITY, a deep learning model that utilizes implicit neural representations (INRs) to address this challenge. Our framework encodes geometric information and physical fields into compact representations and learns a mapping between them to infer the physical fields. We use an airfoil design optimization problem as an example task and we evaluate our approach on the challenging AirfRANS dataset, which closely resembles real-world industrial use-cases. The experimental results demonstrate that our framework achieves state-of-the-art performance by accurately inferring physical fields throughout the volume and surface. Additionally we demonstrate its applicability in contexts such as design exploration and shape optimization: our model can correctly predict drag and lift coefficients while adhering to the equations., Comment: ICML 2023 Workshop on Synergy of Scientific and Machine Learning Modeling

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

We introduce a novel modeling approach for time series imputation and forecasting, tailored to address the challenges often encountered in real-world data, such as irregular samples, missing data, or unaligned measurements from multiple sensors. Our method relies on a continuous-time-dependent model of the series' evolution dynamics. It leverages adaptations of conditional, implicit neural representations for sequential data. A modulation mechanism, driven by a meta-learning algorithm, allows adaptation to unseen samples and extrapolation beyond observed time-windows for long-term predictions. The model provides a highly flexible and unified framework for imputation and forecasting tasks across a wide range of challenging scenarios. It achieves state-of-the-art performance on classical benchmarks and outperforms alternative time-continuous models.

Explainable AI consists in developing mechanisms allowing for an interaction between decision systems and humans by making the decisions of the formers understandable. This is particularly important in sensitive contexts like in the medical domain. We propose a use case study, for skin lesion diagnosis, illustrating how it is possible to provide the practitioner with explanations on the decisions of a state of the art deep neural network classifier trained to characterize skin lesions from examples. Our framework consists of a trained classifier onto which an explanation module operates. The latter is able to offer the practitioner exemplars and counterexemplars for the classification diagnosis thus allowing the physician to interact with the automatic diagnosis system. The exemplars are generated via an adversarial autoencoder. We illustrate the behavior of the system on representative examples., Comment: arXiv admin note: text overlap with arXiv:2111.11863

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

Representing physical signals at different scales is among the most challenging problems in engineering. Several multi-scale modeling tools have been developed to describe physical systems governed by \emph{Partial Differential Equations} (PDEs). These tools are at the crossroad of principled physical models and numerical schema. Recently, data-driven models have been introduced to speed-up the approximation of PDE solutions compared to numerical solvers. Among these recent data-driven methods, neural integral operators are a class that learn a mapping between function spaces. These functions are discretized on graphs (meshes) which are appropriate for modeling interactions in physical phenomena. In this work, we study three multi-resolution schema with integral kernel operators that can be approximated with \emph{Message Passing Graph Neural Networks} (MPGNNs). To validate our study, we make extensive MPGNNs experiments with well-chosen metrics considering steady and unsteady PDEs., Comment: ICLR 2022 Workshop on Geometrical and Topological Representation Learning

Data-driven approaches to modeling physical systems fail to generalize to unseen systems that share the same general dynamics with the learning domain, but correspond to different physical contexts. We propose a new framework for this key problem, context-informed dynamics adaptation (CoDA), which takes into account the distributional shift across systems for fast and efficient adaptation to new dynamics. CoDA leverages multiple environments, each associated to a different dynamic, and learns to condition the dynamics model on contextual parameters, specific to each environment. The conditioning is performed via a hypernetwork, learned jointly with a context vector from observed data. The proposed formulation constrains the search hypothesis space to foster fast adaptation and better generalization across environments. We theoretically motivate our approach and show state-of-the-art generalization results on a set of nonlinear dynamics, representative of a variety of application domains. We also show, on these systems, that new system parameters can be inferred from context vectors with minimal supervision. Code is available at https://github.com/yuan-yin/CoDA ., Comment: Accepted at ICML 2022

This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion, under the assumption that the set of unknown parameter values is finite. This sufficient condition is then verified in the context of a latent price model of market microstructure, yielding consistency of maximum likelihood estimators of the unknown parameters in this model. Finally, we compute the latter estimators using historical financial data taken from the NASDAQ exchange.

A key issue in critical contexts such as medical diagnosis is the interpretability of the deep learning models adopted in decision-making systems. Research in eXplainable Artificial Intelligence (XAI) is trying to solve this issue. However, often XAI approaches are only tested on generalist classifier and do not represent realistic problems such as those of medical diagnosis. In this paper, we analyze a case study on skin lesion images where we customize an existing XAI approach for explaining a deep learning model able to recognize different types of skin lesions. The explanation is formed by synthetic exemplar and counter-exemplar images of skin lesion and offers the practitioner a way to highlight the crucial traits responsible for the classification decision. A survey conducted with domain experts, beginners and unskilled people proof that the usage of explanations increases the trust and confidence in the automatic decision system. Also, an analysis of the latent space adopted by the explainer unveils that some of the most frequent skin lesion classes are distinctly separated. This phenomenon could derive from the intrinsic characteristics of each class and, hopefully, can provide support in the resolution of the most frequent misclassifications by human experts.

To facilitate knowledge reuse in engineering design, several dataset approaches have been proposed and applied by designers. This paper builds a patent-based knowledge graph, patent-KG, to represent the knowledge facts in patents for engineering design. The arising patent-KG approach proposes a new unsupervised mechanism to extract knowledge facts in a patent, by searching the attention graph in language models. This method avoids using expensive labelled data in supervised learning or listing complex syntactic rules in rule-based extraction. The extracted entities are compared with other benchmarks in the criteria of recall rate. The result reaches the highest 0.9 recall rate in the standard list of mechanical engineering related technical terms, which means the highest coverage of engineering words. The extracted relationships are also compared with other benchmarks. The result shows that our method provides more contextual information in relationships, and extracts more relationship types including positional and negation relationships., Comment: delete the weapon examples

When modeling dynamical systems from real-world data samples, the distribution of data often changes according to the environment in which they are captured, and the dynamics of the system itself vary from one environment to another. Generalizing across environments thus challenges the conventional frameworks. The classical settings suggest either considering data as i.i.d. and learning a single model to cover all situations or learning environment-specific models. Both are sub-optimal: the former disregards the discrepancies between environments leading to biased solutions, while the latter does not exploit their potential commonalities and is prone to scarcity problems. We propose LEADS, a novel framework that leverages the commonalities and discrepancies among known environments to improve model generalization. This is achieved with a tailored training formulation aiming at capturing common dynamics within a shared model while additional terms capture environment-specific dynamics. We ground our approach in theory, exhibiting a decrease in sample complexity with our approach and corroborate these results empirically, instantiating it for linear dynamics. Moreover, we concretize this framework for neural networks and evaluate it experimentally on representative families of nonlinear dynamics. We show that this new setting can exploit knowledge extracted from environment-dependent data and improves generalization for both known and novel environments. Code is available at https://github.com/yuan-yin/LEADS., Comment: Published at NeurIPS 2021