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In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally expensive most of all in a real-time and many-query setting. Thus, our main goal is to provide a physics informed learning paradigm to simulate parametrized phenomena in a small amount of time. The physics information will be exploited in many ways, in the loss function (standard physics informed neural networks), as an augmented input (extra feature employment) and as a guideline to build an effective structure for the neural network (physics informed architecture). These three aspects, combined together, will lead to a faster training phase and to a more accurate parametric prediction. The methodology has been tested for several equations and also in an optimal control framework.

There is increasing interest in data-driven approaches for recommending optimal treatment strategies in many chronic disease management and critical care applications. Reinforcement learning methods are well-suited to this sequential decision-making problem, but must be trained and evaluated exclusively on retrospective medical record datasets as direct online exploration is unsafe and infeasible. Despite this requirement, the vast majority of treatment optimization studies use off-policy RL methods (e.g., Double Deep Q Networks (DDQN) or its variants) that are known to perform poorly in purely offline settings. Recent advances in offline RL, such as Conservative Q-Learning (CQL), offer a suitable alternative. But there remain challenges in adapting these approaches to real-world applications where suboptimal examples dominate the retrospective dataset and strict safety constraints need to be satisfied. In this work, we introduce a practical and theoretically grounded transition sampling approach to address action imbalance during offline RL training. We perform extensive experiments on two real-world tasks for diabetes and sepsis treatment optimization to compare performance of the proposed approach against prominent off-policy and offline RL baselines (DDQN and CQL). Across a range of principled and clinically relevant metrics, we show that our proposed approach enables substantial improvements in expected health outcomes and in accordance with relevant practice and safety guidelines.

Training learnable metrics using modern language models has recently emerged as a promising method for the automatic evaluation of machine translation. However, existing human evaluation datasets for text simplification have limited annotations that are based on unitary or outdated models, making them unsuitable for this approach. To address these issues, we introduce the SimpEval corpus that contains: SimpEval_past, comprising 12K human ratings on 2.4K simplifications of 24 past systems, and SimpEval_2022, a challenging simplification benchmark consisting of over 1K human ratings of 360 simplifications including GPT-3.5 generated text. Training on SimpEval, we present LENS, a Learnable Evaluation Metric for Text Simplification. Extensive empirical results show that LENS correlates much better with human judgment than existing metrics, paving the way for future progress in the evaluation of text simplification. We also introduce Rank and Rate, a human evaluation framework that rates simplifications from several models in a list-wise manner using an interactive interface, which ensures both consistency and accuracy in the evaluation process and is used to create the SimpEval datasets.

This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a mixture of Gaussian distributions while satisfying all metric properties. These characteristics enable fast, stable, and efficient calculations, which are highly desirable in real-world signal processing applications. The application in mind is Gaussian Mixture Reduction (GMR), which is widely used in density estimation, recursive tracking, and belief propagation. To address this problem, we developed a novel algorithm dubbed the Optimization-based Greedy GMR (OGGMR), which employs our metric as a criterion to approximate a high-order Gaussian mixture with a lower order. Experimental results show that the OGGMR algorithm is significantly faster and more efficient than state-of-the-art GMR algorithms while retaining the geometric shape of the original mixture.

Over the past decade, Plug-and-Play (PnP) has become a popular method for reconstructing images using a modular framework consisting of a forward and prior model. The great strength of PnP is that an image denoiser can be used as a prior model while the forward model can be implemented using more traditional physics-based approaches. However, a limitation of PnP is that it reconstructs only a single deterministic image. In this paper, we introduce Generative Plug-and-Play (GPnP), a generalization of PnP to sample from the posterior distribution. As with PnP, GPnP has a modular framework using a physics-based forward model and an image denoising prior model. However, in GPnP these models are extended to become proximal generators, which sample from associated distributions. GPnP applies these proximal generators in alternation to produce samples from the posterior. We present experimental simulations using the well-known BM3D denoiser. Our results demonstrate that the GPnP method is robust, easy to implement, and produces intuitively reasonable samples from the posterior for sparse interpolation and tomographic reconstruction. Code to accompany this paper is available at //github.com/gbuzzard/generative-pnp-allerton .

We present VideoFactory, an innovative framework for generating high-quality open-domain videos. VideoFactory excels in producing high-definition (1376x768), widescreen (16:9) videos without watermarks, creating an engaging user experience. Generating videos guided by text instructions poses significant challenges, such as modeling the complex relationship between space and time, and the lack of large-scale text-video paired data. Previous approaches extend pretrained text-to-image generation models by adding temporal 1D convolution/attention modules for video generation. However, these approaches overlook the importance of jointly modeling space and time, inevitably leading to temporal distortions and misalignment between texts and videos. In this paper, we propose a novel approach that strengthens the interaction between spatial and temporal perceptions. In particular, we utilize a swapped cross-attention mechanism in 3D windows that alternates the "query" role between spatial and temporal blocks, enabling mutual reinforcement for each other. To fully unlock model capabilities for high-quality video generation, we curate a large-scale video dataset called HD-VG-130M. This dataset comprises 130 million text-video pairs from the open-domain, ensuring high-definition, widescreen and watermark-free characters. Objective metrics and user studies demonstrate the superiority of our approach in terms of per-frame quality, temporal correlation, and text-video alignment, with clear margins.

We study collaborative normal mean estimation, where $m$ strategic agents collect i.i.d samples from a normal distribution $\mathcal{N}(\mu, \sigma^2)$ at a cost. They all wish to estimate the mean $\mu$. By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes. We design a novel mechanism that overcomes these challenges via two key techniques: first, when sharing the others' data with an agent, the mechanism corrupts this dataset proportional to how much the data reported by the agent differs from the others; second, we design minimax optimal estimators for the corrupted dataset. Our mechanism, which is incentive compatible and individually rational, achieves a social penalty (sum of all agents' estimation errors and data collection costs) that is at most a factor 2 of the global minimum. When applied to high dimensional (non-Gaussian) distributions with bounded variance, this mechanism retains these three properties, but with slightly weaker results. Finally, in two special cases where we restrict the strategy space of the agents, we design mechanisms that essentially achieve the global minimum.

The determination of biological brain age is a crucial biomarker in the assessment of neurological disorders and understanding of the morphological changes that occur during aging. Various machine learning models have been proposed for estimating brain age through Magnetic Resonance Imaging (MRI) of healthy controls. However, developing a robust brain age estimation (BAE) framework has been challenging due to the selection of appropriate MRI-derived features and the high cost of MRI acquisition. In this study, we present a novel BAE framework using the Open Big Healthy Brain (OpenBHB) dataset, which is a new multi-site and publicly available benchmark dataset that includes region-wise feature metrics derived from T1-weighted (T1-w) brain MRI scans of 3965 healthy controls aged between 6 to 86 years. Our approach integrates three different MRI-derived region-wise features and different regression models, resulting in a highly accurate brain age estimation with a Mean Absolute Error (MAE) of 3.25 years, demonstrating the framework's robustness. We also analyze our model's regression-based performance on gender-wise (male and female) healthy test groups. The proposed BAE framework provides a new approach for estimating brain age, which has important implications for the understanding of neurological disorders and age-related brain changes.

Generative AI models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of three-dimensional (3D) shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new two-dimensional (2D) representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 9,070 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics (CFD) simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an $R^2$ value above 0.84 for various car categories. Moreover, the proposed representation method can be generalized to many other product categories beyond cars. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as Stable Diffusion) and a significant step towards the automatic generation of drag-optimized car designs. We have made the dataset and code publicly available at //decode.mit.edu/projects/dragprediction/.

Human pose estimation aims to locate the human body parts and build human body representation (e.g., body skeleton) from input data such as images and videos. It has drawn increasing attention during the past decade and has been utilized in a wide range of applications including human-computer interaction, motion analysis, augmented reality, and virtual reality. Although the recently developed deep learning-based solutions have achieved high performance in human pose estimation, there still remain challenges due to insufficient training data, depth ambiguities, and occlusions. The goal of this survey paper is to provide a comprehensive review of recent deep learning-based solutions for both 2D and 3D pose estimation via a systematic analysis and comparison of these solutions based on their input data and inference procedures. More than 240 research papers since 2014 are covered in this survey. Furthermore, 2D and 3D human pose estimation datasets and evaluation metrics are included. Quantitative performance comparisons of the reviewed methods on popular datasets are summarized and discussed. Finally, the challenges involved, applications, and future research directions are concluded. We also provide a regularly updated project page on: \url{//github.com/zczcwh/DL-HPE}