Knowledge-guided Machine Learning: Current Trends and Future Prospects

This paper presents an overview of scientific modeling and discusses the complementary strengths and weaknesses of ML methods for scientific modeling in comparison to process-based models. It also provides an introduction to the current state of research in the emerging field of scientific knowledge-guided machine learning (KGML) that aims to use both scientific knowledge and data in ML frameworks to achieve better generalizability, scientific consistency, and explainability of results. We discuss different facets of KGML research in terms of the type of scientific knowledge used, the form of knowledge-ML integration explored, and the method for incorporating scientific knowledge in ML. We also discuss some of the common categories of use cases in environmental sciences where KGML methods are being developed, using illustrative examples in each category.

A Simple Interpretable Transformer for Fine-Grained Image Classification and Analysis

We present a novel usage of Transformers to make image classification interpretable. Unlike mainstream classifiers that wait until the last fully-connected layer to incorporate class information to make predictions, we investigate a proactive approach, asking each class to search for itself in an image. We realize this idea via a Transformer encoder-decoder inspired by DEtection TRansformer (DETR). We learn ``class-specific'' queries (one for each class) as input to the decoder, enabling each class to localize its patterns in an image via cross-attention. We name our approach INterpretable TRansformer (INTR), which is fairly easy to implement and exhibits several compelling properties. We show that INTR intrinsically encourages each class to attend distinctively; the cross-attention weights thus provide a faithful interpretation of the prediction. Interestingly, via ``multi-head'' cross-attention, INTR could identify different ``attributes'' of a class, making it particularly suitable for fine-grained classification and analysis, which we demonstrate on eight datasets. Our code and pre-trained model are publicly accessible at https://github.com/Imageomics/INTR.

MEMTRACK: A Deep Learning-Based Approach to Microrobot Tracking in Dense and Low-Contrast Environments

Tracking microrobots is challenging, considering their minute size and high speed. As the field progresses towards developing microrobots for biomedical applications and conducting mechanistic studies in physiologically relevant media (e.g., collagen), this challenge is exacerbated by the dense surrounding environments with feature size and shape comparable to microrobots. Herein, we report Motion Enhanced Multi-level Tracker (MEMTrack), a robust pipeline for detecting and tracking microrobots using synthetic motion features, deep learning-based object detection, and a modified Simple Online and Real-time Tracking (SORT) algorithm with interpolation for tracking. Our object detection approach combines different models based on the object's motion pattern. We trained and validated our model using bacterial micro-motors in collagen (tissue phantom) and tested it in collagen and aqueous media. We demonstrate that MEMTrack accurately tracks even the most challenging bacteria missed by skilled human annotators, achieving precision and recall of 77% and 48% in collagen and 94% and 35% in liquid media, respectively. Moreover, we show that MEMTrack can quantify average bacteria speed with no statistically significant difference from the laboriously-produced manual tracking data. MEMTrack represents a significant contribution to microrobot localization and tracking, and opens the potential for vision-based deep learning approaches to microrobot control in dense and low-contrast settings. All source code for training and testing MEMTrack and reproducing the results of the paper have been made publicly available https://github.com/sawhney-medha/MEMTrack.

Neuro-Visualizer: An Auto-encoder-based Loss Landscape Visualization Method

In recent years, there has been a growing interest in visualizing the loss landscape of neural networks. Linear landscape visualization methods, such as principal component analysis, have become widely used as they intuitively help researchers study neural networks and their training process. However, these linear methods suffer from limitations and drawbacks due to their lack of flexibility and low fidelity at representing the high dimensional landscape. In this paper, we present a novel auto-encoder-based non-linear landscape visualization method called Neuro-Visualizer that addresses these shortcoming and provides useful insights about neural network loss landscapes. To demonstrate its potential, we run experiments on a variety of problems in two separate applications of knowledge-guided machine learning (KGML). Our findings show that Neuro-Visualizer outperforms other linear and non-linear baselines and helps corroborate, and sometime challenge, claims proposed by machine learning community. All code and data used in the experiments of this paper are available at an anonymous link https://anonymous.4open.science/r/NeuroVisualizer-FDD6

Beyond Discriminative Regions: Saliency Maps as Alternatives to CAMs for Weakly Supervised Semantic Segmentation

In recent years, several Weakly Supervised Semantic Segmentation (WS3) methods have been proposed that use class activation maps (CAMs) generated by a classifier to produce pseudo-ground truths for training segmentation models. While CAMs are good at highlighting discriminative regions (DR) of an image, they are known to disregard regions of the object that do not contribute to the classifier's prediction, termed non-discriminative regions (NDR). In contrast, attribution methods such as saliency maps provide an alternative approach for assigning a score to every pixel based on its contribution to the classification prediction. This paper provides a comprehensive comparison between saliencies and CAMs for WS3. Our study includes multiple perspectives on understanding their similarities and dissimilarities. Moreover, we provide new evaluation metrics that perform a comprehensive assessment of WS3 performance of alternative methods w.r.t. CAMs. We demonstrate the effectiveness of saliencies in addressing the limitation of CAMs through our empirical studies on benchmark datasets. Furthermore, we propose random cropping as a stochastic aggregation technique that improves the performance of saliency, making it a strong alternative to CAM for WS3.

Discovering Novel Biological Traits From Images Using Phylogeny-Guided Neural Networks

Discovering evolutionary traits that are heritable across species on the tree of life (also referred to as a phylogenetic tree) is of great interest to biologists to understand how organisms diversify and evolve. However, the measurement of traits is often a subjective and labor-intensive process, making trait discovery a highly label-scarce problem. We present a novel approach for discovering evolutionary traits directly from images without relying on trait labels. Our proposed approach, Phylo-NN, encodes the image of an organism into a sequence of quantized feature vectors -- or codes -- where different segments of the sequence capture evolutionary signals at varying ancestry levels in the phylogeny. We demonstrate the effectiveness of our approach in producing biologically meaningful results in a number of downstream tasks including species image generation and species-to-species image translation, using fish species as a target example.

Let There Be Order: Rethinking Ordering in Autoregressive Graph Generation

Conditional graph generation tasks involve training a model to generate a graph given a set of input conditions. Many previous studies employ autoregressive models to incrementally generate graph components such as nodes and edges. However, as graphs typically lack a natural ordering among their components, converting a graph into a sequence of tokens is not straightforward. While prior works mostly rely on conventional heuristics or graph traversal methods like breadth-first search (BFS) or depth-first search (DFS) to convert graphs to sequences, the impact of ordering on graph generation has largely been unexplored. This paper contributes to this problem by: (1) highlighting the crucial role of ordering in autoregressive graph generation models, (2) proposing a novel theoretical framework that perceives ordering as a dimensionality reduction problem, thereby facilitating a deeper understanding of the relationship between orderings and generated graph accuracy, and (3) introducing "latent sort," a learning-based ordering scheme to perform dimensionality reduction of graph tokens. Our experimental results showcase the effectiveness of latent sort across a wide range of graph generation tasks, encouraging future works to further explore and develop learning-based ordering schemes for autoregressive graph generation.

Multi-task Learning for Source Attribution and Field Reconstruction for Methane Monitoring

Inferring the source information of greenhouse gases, such as methane, from spatially sparse sensor observations is an essential element in mitigating climate change. While it is well understood that the complex behavior of the atmospheric dispersion of such pollutants is governed by the Advection-Diffusion equation, it is difficult to directly apply the governing equations to identify the source location and magnitude (inverse problem) because of the spatially sparse and noisy observations, i.e., the pollution concentration is known only at the sensor locations and sensors sensitivity is limited. Here, we develop a multi-task learning framework that can provide high-fidelity reconstruction of the concentration field and identify emission characteristics of the pollution sources such as their location, emission strength, etc. from sparse sensor observations. We demonstrate that our proposed framework is able to achieve accurate reconstruction of the methane concentrations from sparse sensor measurements as well as precisely pin-point the location and emission strength of these pollution sources.

Rethinking the Importance of Sampling in Physics-informed Neural Networks

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving partial differential equations (PDEs) in a variety of domains. While previous research in PINNs has mainly focused on constructing and balancing loss functions during training to avoid poor minima, the effect of sampling collocation points on the performance of PINNs has largely been overlooked. In this work, we find that the performance of PINNs can vary significantly with different sampling strategies, and using a fixed set of collocation points can be quite detrimental to the convergence of PINNs to the correct solution. In particular, (1) we hypothesize that training of PINNs rely on successful "propagation" of solution from initial and/or boundary condition points to interior points, and PINNs with poor sampling strategies can get stuck at trivial solutions if there are \textit{propagation failures}. (2) We demonstrate that propagation failures are characterized by highly imbalanced PDE residual fields where very high residuals are observed over very narrow regions. (3) To mitigate propagation failure, we propose a novel \textit{evolutionary sampling} (Evo) method that can incrementally accumulate collocation points in regions of high PDE residuals. We further provide an extension of Evo to respect the principle of causality while solving time-dependent PDEs. We empirically demonstrate the efficacy and efficiency of our proposed methods in a variety of PDE problems.

Physics-Guided Problem Decomposition for Scaling Deep Learning of High-dimensional Eigen-Solvers: The Case of Schrödinger's Equation

Given their ability to effectively learn non-linear mappings and perform fast inference, deep neural networks (NNs) have been proposed as a viable alternative to traditional simulation-driven approaches for solving high-dimensional eigenvalue equations (HDEs), which are the foundation for many scientific applications. Unfortunately, for the learned models in these scientific applications to achieve generalization, a large, diverse, and preferably annotated dataset is typically needed and is computationally expensive to obtain. Furthermore, the learned models tend to be memory- and compute-intensive primarily due to the size of the output layer. While generalization, especially extrapolation, with scarce data has been attempted by imposing physical constraints in the form of physics loss, the problem of model scalability has remained. In this paper, we alleviate the compute bottleneck in the output layer by using physics knowledge to decompose the complex regression task of predicting the high-dimensional eigenvectors into multiple simpler sub-tasks, each of which are learned by a simple "expert" network. We call the resulting architecture of specialized experts Physics-Guided Mixture-of-Experts (PG-MoE). We demonstrate the efficacy of such physics-guided problem decomposition for the case of the Schr\"{o}dinger's Equation in Quantum Mechanics. Our proposed PG-MoE model predicts the ground-state solution, i.e., the eigenvector that corresponds to the smallest possible eigenvalue. The model is 150x smaller than the network trained to learn the complex task while being competitive in generalization. To improve the generalization of the PG-MoE, we also employ a physics-guided loss function based on variational energy, which by quantum mechanics principles is minimized iff the output is the ground-state solution.