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Current physics-informed (standard or operator) neural networks still rely on accurately learning the initial conditions of the system they are solving. In contrast, standard numerical methods evolve such initial conditions without needing to learn these. In this study, we propose to improve current physics-informed deep learning strategies such that initial conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a DeepONet is applied multiple times to time step a solution, the resulting function is continuous.

Research on pronunciation assessment systems focuses on utilizing phonetic and phonological aspects of non-native (L2) speech, often neglecting the rich layer of information hidden within the non-verbal cues. In this study, we proposed a novel pronunciation assessment framework, IntraVerbalPA. % The framework innovatively incorporates both fine-grained frame- and abstract utterance-level non-verbal cues, alongside the conventional speech and phoneme representations. Additionally, we introduce ''Goodness of phonemic-duration'' metric to effectively model duration distribution within the framework. Our results validate the effectiveness of the proposed IntraVerbalPA framework and its individual components, yielding performance that either matches or outperforms existing research works.

Decoding language from neural signals holds considerable theoretical and practical importance. Previous research has indicated the feasibility of decoding text or speech from invasive neural signals. However, when using non-invasive neural signals, significant challenges are encountered due to their low quality. In this study, we proposed a data-driven approach for decoding semantic of language from Magnetoencephalography (MEG) signals recorded while subjects were listening to continuous speech. First, a multi-subject decoding model was trained using contrastive learning to reconstruct continuous word embeddings from MEG data. Subsequently, a beam search algorithm was adopted to generate text sequences based on the reconstructed word embeddings. Given a candidate sentence in the beam, a language model was used to predict the subsequent words. The word embeddings of the subsequent words were correlated with the reconstructed word embedding. These correlations were then used as a measure of the probability for the next word. The results showed that the proposed continuous word embedding model can effectively leverage both subject-specific and subject-shared information. Additionally, the decoded text exhibited significant similarity to the target text, with an average BERTScore of 0.816, a score comparable to that in the previous fMRI study.

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge, especially when encountering noisy observations and no prior knowledge available. This study proposes R-DISCOVER, a framework designed to robustly uncover open-form partial differential equations (PDEs) from limited and noisy data. The framework operates through two alternating update processes: discovering and embedding. The discovering phase employs symbolic representation and a reinforcement learning (RL)-guided hybrid PDE generator to efficiently produce diverse open-form PDEs with tree structures. A neural network-based predictive model fits the system response and serves as the reward evaluator for the generated PDEs. PDEs with superior fits are utilized to iteratively optimize the generator via the RL method and the best-performing PDE is selected by a parameter-free stability metric. The embedding phase integrates the initially identified PDE from the discovering process as a physical constraint into the predictive model for robust training. The traversal of PDE trees automates the construction of the computational graph and the embedding process without human intervention. Numerical experiments demonstrate our framework's capability to uncover governing equations from nonlinear dynamic systems with limited and highly noisy data and outperform other physics-informed neural network-based discovery methods. This work opens new potential for exploring real-world systems with limited understanding.

A method for sound field decomposition based on neural networks is proposed. The method comprises two stages: a sound field separation stage and a single-source localization stage. In the first stage, the sound pressure at microphones synthesized by multiple sources is separated into one excited by each sound source. In the second stage, the source location is obtained as a regression from the sound pressure at microphones consisting of a single sound source. The estimated location is not affected by discretization because the second stage is designed as a regression rather than a classification. Datasets are generated by simulation using Green's function, and the neural network is trained for each frequency. Numerical experiments reveal that, compared with conventional methods, the proposed method can achieve higher source-localization accuracy and higher sound-field-reconstruction accuracy.

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds. This is closely related to dynamical low-rank approximation (DLRA) techniques. In fact, any retraction leads to a numerical integrator and, vice versa, certain DLRA techniques bear a direct relation with retractions. As an example for the latter, we introduce a new retraction, called KLS retraction, that is derived from the so-called unconventional integrator for DLRA. We also illustrate how retractions can be used to recover known DLRA techniques and to design new ones. In particular, this work introduces two novel numerical integration schemes that apply to differential equations on general manifolds: the accelerated forward Euler (AFE) method and the Ralston-Hermite (RH) method. Both methods build on retractions by using them as a tool for approximating curves on manifolds. The two methods are proven to have local truncation error of order three. Numerical experiments on classical DLRA examples highlight the advantages and shortcomings of these new methods.

Autonomous inspection tasks necessitate effective path-planning mechanisms to efficiently gather observations from points of interest (POI). However, localization errors commonly encountered in urban environments can introduce execution uncertainty, posing challenges to the successful completion of such tasks. To tackle these challenges, we present IRIS-under uncertainty (IRIS-U^2), an extension of the incremental random inspection-roadmap search (IRIS) algorithm, that addresses the offline planning problem via an A*-based approach, where the planning process occurs prior the online execution. The key insight behind IRIS-U^2 is transforming the computed localization uncertainty, obtained through Monte Carlo (MC) sampling, into a POI probability. IRIS-U^2 offers insights into the expected performance of the execution task by providing confidence intervals (CI) for the expected coverage, expected path length, and collision probability, which becomes progressively tighter as the number of MC samples increase. The efficacy of IRIS-U^2 is demonstrated through a case study focusing on structural inspections of bridges. Our approach exhibits improved expected coverage, reduced collision probability, and yields increasingly-precise CIs as the number of MC samples grows. Furthermore, we emphasize the potential advantages of computing bounded sub-optimal solutions to reduce computation time while still maintaining the same CI boundaries.

Confounder selection, namely choosing a set of covariates to control for confounding between a treatment and an outcome, is arguably the most important step in the design of observational studies. Previous methods, such as Pearl's celebrated back-door criterion, typically require pre-specifying a causal graph, which can often be difficult in practice. We propose an interactive procedure for confounder selection that does not require pre-specifying the graph or the set of observed variables. This procedure iteratively expands the causal graph by finding what we call "primary adjustment sets" for a pair of possibly confounded variables. This can be viewed as inverting a sequence of latent projections of the underlying causal graph. Structural information in the form of primary adjustment sets is elicited from the user, bit by bit, until either a set of covariates are found to control for confounding or it can be determined that no such set exists. We show that if the user correctly specifies the primary adjustment sets in every step, our procedure is both sound and complete.

Next Point-of-Interest (POI) recommendation is a critical task in location-based services that aim to provide personalized suggestions for the user's next destination. Previous works on POI recommendation have laid focused on modeling the user's spatial preference. However, existing works that leverage spatial information are only based on the aggregation of users' previous visited positions, which discourages the model from recommending POIs in novel areas. This trait of position-based methods will harm the model's performance in many situations. Additionally, incorporating sequential information into the user's spatial preference remains a challenge. In this paper, we propose Diff-POI: a Diffusion-based model that samples the user's spatial preference for the next POI recommendation. Inspired by the wide application of diffusion algorithm in sampling from distributions, Diff-POI encodes the user's visiting sequence and spatial character with two tailor-designed graph encoding modules, followed by a diffusion-based sampling strategy to explore the user's spatial visiting trends. We leverage the diffusion process and its reversed form to sample from the posterior distribution and optimized the corresponding score function. We design a joint training and inference framework to optimize and evaluate the proposed Diff-POI. Extensive experiments on four real-world POI recommendation datasets demonstrate the superiority of our Diff-POI over state-of-the-art baseline methods. Further ablation and parameter studies on Diff-POI reveal the functionality and effectiveness of the proposed diffusion-based sampling strategy for addressing the limitations of existing methods.

Radiologist is "doctor's doctor", biomedical image segmentation plays a central role in quantitative analysis, clinical diagnosis, and medical intervention. In the light of the fully convolutional networks (FCN) and U-Net, deep convolutional networks (DNNs) have made significant contributions in biomedical image segmentation applications. In this paper, based on U-Net, we propose MDUnet, a multi-scale densely connected U-net for biomedical image segmentation. we propose three different multi-scale dense connections for U shaped architectures encoder, decoder and across them. The highlights of our architecture is directly fuses the neighboring different scale feature maps from both higher layers and lower layers to strengthen feature propagation in current layer. Which can largely improves the information flow encoder, decoder and across them. Multi-scale dense connections, which means containing shorter connections between layers close to the input and output, also makes much deeper U-net possible. We adopt the optimal model based on the experiment and propose a novel Multi-scale Dense U-Net (MDU-Net) architecture with quantization. Which reduce overfitting in MDU-Net for better accuracy. We evaluate our purpose model on the MICCAI 2015 Gland Segmentation dataset (GlaS). The three multi-scale dense connections improve U-net performance by up to 1.8% on test A and 3.5% on test B in the MICCAI Gland dataset. Meanwhile the MDU-net with quantization achieves the superiority over U-Net performance by up to 3% on test A and 4.1% on test B.