In recent years, the increasing threat of devastating wildfires has underscored the need for effective prescribed fire management. Process-based computer simulations have traditionally been employed to plan prescribed fires for wildfire prevention. However, even simplified process models like QUIC-Fire are too compute-intensive to be used for real-time decision-making, especially when weather conditions change rapidly. Traditional ML methods used for fire modeling offer computational speedup but struggle with physically inconsistent predictions, biased predictions due to class imbalance, biased estimates for fire spread metrics (e.g., burned area, rate of spread), and generalizability in out-of-distribution wind conditions. This paper introduces a novel machine learning (ML) framework that enables rapid emulation of prescribed fires while addressing these concerns. By incorporating domain knowledge, the proposed method helps reduce physical inconsistencies in fuel density estimates in data-scarce scenarios. To overcome the majority class bias in predictions, we leverage pre-existing source domain data to augment training data and learn the spread of fire more effectively. Finally, we overcome the problem of biased estimation of fire spread metrics by incorporating a hierarchical modeling structure to capture the interdependence in fuel density and burned area. Notably, improvement in fire metric (e.g., burned area) estimates offered by our framework makes it useful for fire managers, who often rely on these fire metric estimates to make decisions about prescribed burn management. Furthermore, our framework exhibits better generalization capabilities than the other ML-based fire modeling methods across diverse wind conditions and ignition patterns.

Causal DAGs(Directed Acyclic Graphs) are usually considered in a 2D plane. Edges indicate causal effects' directions and imply their corresponding time-passings. Due to the natural restriction of statistical models, effect estimation is usually approximated by averaging the individuals' correlations, i.e., observational changes over a specific time. However, in the context of Machine Learning on large-scale questions with complex DAGs, such slight biases can snowball to distort global models - More importantly, it has practically impeded the development of AI, for instance, the weak generalizability of causal models. In this paper, we redefine causal DAG as \emph{do-DAG}, in which variables' values are no longer time-stamp-dependent, and timelines can be seen as axes. By geometric explanation of multi-dimensional do-DAG, we identify the \emph{Causal Representation Bias} and its necessary factors, differentiated from common confounding biases. Accordingly, a DL(Deep Learning)-based framework will be proposed as the general solution, along with a realization method and experiments to verify its feasibility.

In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to mini-batch training, temporal relationships between training segments within the batch (intra-batch) as well as between batches (inter-batch) are not considered, which can lead to limited performance. Stateful RNNs aim to address this issue by passing hidden states between batches. Since Stateful RNNs ignore intra-batch temporal dependency, there exists a trade-off between training stability and capturing temporal dependency. In this paper, we provide a quantitative comparison of different Stateful RNN modeling strategies, and propose two strategies to enforce both intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by defining a batch as a temporally ordered set of training segments, which enables intra-batch sharing of temporal information. While this approach significantly improves the performance, it leads to much larger training times due to highly sequential training. To address this issue, we further propose a new strategy which augments a training segment with an initial value of the target variable from the timestep right before the starting of the training segment. In other words, we provide an initial value of the target variable as additional input so that the network can focus on learning changes relative to that initial value. By using this strategy, samples can be passed in any order (mini-batch training) which significantly reduces the training time while maintaining the performance. In demonstrating our approach in hydrological modeling, we observe that the most significant gains in predictive accuracy occur when these methods are applied to state variables whose values change more slowly, such as soil water and snowpack, rather than continuously moving flux variables such as streamflow.

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. The PGRNN has the flexibility to incorporate additional physical constraints and we incorporate a density-depth relationship. Both enhancements further improve PGRNN performance. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine.

Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of data science models in enabling scientific discovery. The overarching vision of TGDS is to introduce scientific consistency as an essential component for learning generalizable models. Further, by producing scientifically interpretable models, TGDS aims to advance our scientific understanding by discovering novel domain insights. Indeed, the paradigm of TGDS has started to gain prominence in a number of scientific disciplines such as turbulence modeling, material discovery, quantum chemistry, bio-medical science, bio-marker discovery, climate science, and hydrology. In this paper, we formally conceptualize the paradigm of TGDS and present a taxonomy of research themes in TGDS. We describe several approaches for integrating domain knowledge in different research themes using illustrative examples from different disciplines. We also highlight some of the promising avenues of novel research for realizing the full potential of theory-guided data science.