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Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within PINNs to robustly accommodate geometric variations. Our method incorporates a diffeomorphism as a mapping of a reference domain and adapts the derivative computation of the physics-informed loss function. This generalizes the applicability of PINNs not only to smoothly deformed domains, but also to lower-dimensional manifolds and allows for direct shape optimization while training the network. We demonstrate the effectivity of our approach on several problems: (i) Eikonal equation on Archimedean spiral, (ii) Poisson problem on surface manifold, (iii) Incompressible Stokes flow in deformed tube, and (iv) Shape optimization with Laplace operator. Through these examples, we demonstrate the enhanced flexibility over traditional PINNs, especially under geometric variations. The proposed framework presents an outlook for training deep neural operators over parametrized geometries, paving the way for advanced modeling with PDEs on complex geometries in science and engineering.

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution generating the data. We observe that the maximum likelihood problem for the Cauchy distributions, which have particularly heavy tails, is geodesically convex and therefore efficiently solvable (Cauchy distributions are parametrized by the upper half plane, i.e. by the hyperbolic plane). Moreover, it has an appealing geometrical meaning: the datapoints, living on the boundary of the hyperbolic plane, are attracting the parameter by unit forces, and we search the point where these forces are in equilibrium. This picture generalizes to several classes of multivariate distributions with heavy tails, including, in particular, the multivariate Cauchy distributions. The hyperbolic plane gets replaced by symmetric spaces of noncompact type. Geodesic convexity gives us an efficient numerical solution of the maximum likelihood problem for these distribution classes. This can then be used for robust estimates of location and spread, thanks to the heavy tails of these distributions.

In a number of information retrieval applications (e.g., patent search, literature review, due diligence, etc.), preventing false negatives is more important than preventing false positives. However, approaches designed to reduce review effort (like "technology assisted review") can create false negatives, since they are often based on active learning systems that exclude documents automatically based on user feedback. Therefore, this research proposes a more recall-oriented approach to reducing review effort. More specifically, through iteratively re-ranking the relevance rankings based on user feedback, which is also referred to as relevance feedback. In our proposed method, the relevance rankings are produced by a BERT-based dense-vector search and the relevance feedback is based on cumulatively summing the queried and selected embeddings. Our results show that this method can reduce review effort between 17.85% and 59.04%, compared to a baseline approach (of no feedback), given a fixed recall target

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear behavior has been a key challenge in predicting whether all oscillators in such a system will eventually synchronize. In this paper, we demonstrate that, surprisingly, such nonlinear behavior of coupled oscillators can be effectively linearized in certain latent dynamic spaces. The key insight is that there is a small number of `latent dynamics filters', each with a specific association with synchronizing and non-synchronizing dynamics on subgraphs so that any observed dynamics on subgraphs can be approximated by a suitable linear combination of such elementary dynamic patterns. Taking an ensemble of subgraph-level predictions provides an interpretable predictor for whether the system on the whole graph reaches global synchronization. We propose algorithms based on supervised matrix factorization to learn such latent dynamics filters. We demonstrate that our method performs competitively in synchronization prediction tasks against baselines and black-box classification algorithms, despite its simple and interpretable architecture.

Appendicitis is among the most frequent reasons for pediatric abdominal surgeries. Previous decision support systems for appendicitis have focused on clinical, laboratory, scoring, and computed tomography data and have ignored abdominal ultrasound, despite its noninvasive nature and widespread availability. In this work, we present interpretable machine learning models for predicting the diagnosis, management and severity of suspected appendicitis using ultrasound images. Our approach utilizes concept bottleneck models (CBM) that facilitate interpretation and interaction with high-level concepts understandable to clinicians. Furthermore, we extend CBMs to prediction problems with multiple views and incomplete concept sets. Our models were trained on a dataset comprising 579 pediatric patients with 1709 ultrasound images accompanied by clinical and laboratory data. Results show that our proposed method enables clinicians to utilize a human-understandable and intervenable predictive model without compromising performance or requiring time-consuming image annotation when deployed. For predicting the diagnosis, the extended multiview CBM attained an AUROC of 0.80 and an AUPR of 0.92, performing comparably to similar black-box neural networks trained and tested on the same dataset.

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions between interactive entities. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. The associated challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. We further show that when combined with known constraints, it allows us, for example, to discover physics-consistent interaction laws of particle systems. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning.

Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).

End-to-end relation extraction (E2ERE) is an important and realistic application of natural language processing (NLP) in biomedicine. In this paper, we aim to compare three prevailing paradigms for E2ERE using a complex dataset focused on rare diseases involving discontinuous and nested entities. We use the RareDis information extraction dataset to evaluate three competing approaches (for E2ERE): NER $\rightarrow$ RE pipelines, joint sequence to sequence models, and generative pre-trained transformer (GPT) models. We use comparable state-of-the-art models and best practices for each of these approaches and conduct error analyses to assess their failure modes. Our findings reveal that pipeline models are still the best, while sequence-to-sequence models are not far behind; GPT models with eight times as many parameters are worse than even sequence-to-sequence models and lose to pipeline models by over 10 F1 points. Partial matches and discontinuous entities caused many NER errors contributing to lower overall E2E performances. We also verify these findings on a second E2ERE dataset for chemical-protein interactions. Although generative LM-based methods are more suitable for zero-shot settings, when training data is available, our results show that it is better to work with more conventional models trained and tailored for E2ERE. More innovative methods are needed to marry the best of the both worlds from smaller encoder-decoder pipeline models and the larger GPT models to improve E2ERE. As of now, we see that well designed pipeline models offer substantial performance gains at a lower cost and carbon footprint for E2ERE. Our contribution is also the first to conduct E2ERE for the RareDis dataset.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.