Accelerating ecological connectivity analysis with graph neural networks

Wed, 19 Nov 2025 00:00:00 +0000

Landscape fragmentation represents a primary driver of biodiversity loss, leading to genetic impoverishment in ecological populations and reduced species resilience to environmental perturbations. Mitigating these effects requires identifying priority areas that function as ecological corridors to maintain connectivity (for protection) and bottleneck regions (for restoration) to enhance ecological connectivity across fragmented landscapes.

Central to this challenge is the modeling of gene flow dynamics. Gene flow between populations can be predicted through resistive distance [1], a measure of distance on a graph, applied to a spatial graph representing the landscape.

In such spatial graphs, vertices represent discrete locations and edges are weighted by resistance values that quantify the resistance to movement imposed by landscape features for a given species. A fundamental challenge in current approaches lies in incorporating fine-grained landscape features (roads, buildings, land cover heterogeneity) into gene flow predictions while maintaining computational tractability.

State-of-the-art methods [2] typically represent each landscape cell as a graph vertex, resulting in prohibitive computational costs for resistance distance calculations that constrain the spatial resolution achievable for predictions.

This project explores a novel approach leveraging graph neural networks (GNNs) to address these computational limitations. GNNs provide a principled framework for learning embeddings that map fine-scale landscape features onto lower-dimensional graph representations, potentially enabling accurate gene flow predictions with significantly reduced computational overhead compared to traditional methods. Key research directions include: (1) theoretical or empirical identification of optimal graph coarsening strategies that preserve resistance distance accuracy, (2) formal characterization of approximation error bounds when computing resistive distances on reduced graphs, and (3) validation on synthetic and real-world ecological datasets with empirical genetic connectivity measurements.

The project scope is flexible and can emphasize theoretical foundations or empirical applications depending on the student’s background and interests.

References

[1] Klein, D. J., & Randić, M. (2008). Minimizing Effective Resistance of a Graph. SIAM Review. https://epubs.siam.org/doi/abs/10.1137/050645452

[2] Ghosh, A., Boyd, S., Saberi, A. (2021). Graph Learning for Inverse Landscape Genetics. AAAI. https://ojs.aaai.org/index.php/AAAI/article/view/17731

Developing an algebraic multigrid solver in JAX

Wed, 19 Nov 2025 00:00:00 +0000

Multigrid methods represent the state-of-the-art for solving large-scale linear systems arising from discretized partial differential equations, offering optimal computational complexity for many problem classes.

Established implementations such as pyAMG and AMG.jl provide robust solvers but lack two critical capabilities for modern scientific machine learning: GPU acceleration and automatic differentiation compatibility. These features are essential for scientific machine learning workflows where differentiable simulation components (e.g., neural networks embedded in physical models) require efficient iterative solves with gradient backpropagation for end-to-end optimization.

This project aims to develop an algebraic multigrid (AMG) solver in JAX that natively supports automatic differentiation and GPU acceleration. The work involves analyzing existing Python and Julia implementations to design an architecture compatible with JAX’s functional programming paradigm and just-in-time compilation model. A successful implementation could have substantial impact on the JAX ecosystem, from accelerating finite element packages to accelerating ecological connectivity analysis tools.

The project scope is flexible and can emphasize software engineering or algorithmic optimization depending on the student’s background and interests. Prior experience with JAX or advanced numerical linear algebra is beneficial but not required; students will gain deep expertise in iterative solvers, functional programming patterns, and best practices for scientific open-source software development.

Student Projects | Victor Boussange

Accelerating ecological connectivity analysis with graph neural networks

References

Developing an algebraic multigrid solver in JAX