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Knowledge-Inclusive Adaptive Physics-Informed Neural Network for Microbial Interaction Modelling

This paper proposes a Knowledge-Inclusive Adaptive Physics-Informed Neural Network (PINN) framework that enhances microbial interaction modeling by integrating auxiliary knowledge from literature and network structures with experimental data, achieving significant accuracy improvements over state-of-the-art methods in predicting microbial community dynamics.

Original authors: Ravisha Rupasinghe, Rajith Vidanaarachchi, Asela Hevapathige, Sachith Seneviratne, Sen-Lin Tang, Saman Halgamuge

Published 2026-06-09

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CC BY 4.0

Original authors: Ravisha Rupasinghe, Rajith Vidanaarachchi, Asela Hevapathige, Sachith Seneviratne, Sen-Lin Tang, Saman Halgamuge

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict how a group of people in a crowded room will interact. You have a video camera recording who is standing where and how many people are in the room (this is your experimental data). But you also know that people react differently depending on the music playing, the temperature, or if they just heard some gossip (this is the contextual knowledge).

For a long time, scientists trying to model how microbes (tiny living organisms) interact in places like the human gut or plant roots have only looked at the "video camera" data. They used a standard mathematical recipe called the Generalised Lotka-Volterra (gLV) equation to guess how these microbes influence each other. However, this recipe often failed because it didn't know about the "gossip" or the "music"—the external factors that change how microbes behave.

This paper introduces a new, smarter way to model these interactions called KI-APINN (Knowledge-Inclusive Adaptive Physics-Informed Neural Network). Here is how it works, broken down into simple concepts:

1. The Problem: The "Blind" Mathematician

Imagine a mathematician trying to solve a puzzle but is only allowed to look at the final picture, not the pieces or the instructions. They have to guess the rules of the game just by looking at the outcome.

The Old Way: Previous methods tried to learn the rules of microbial interaction only by watching the microbes grow and shrink over time. They often got the rules wrong because they ignored the vast amount of scientific literature that already exists about what these microbes do.
The Gap: The "rules" (parameters) of microbial life aren't fixed; they change based on the environment. A microbe might be friendly in one situation and aggressive in another.

2. The Solution: The "Well-Read" Detective

The authors built a system that acts like a detective who doesn't just watch the crime scene (the data) but also reads the entire library of police reports (scientific literature) before making a guess.

The "Physics" Part: They still use the standard mathematical recipe (gLV) because it's a proven way to describe how living things grow and compete. This ensures the model stays grounded in biological reality.
The "Knowledge" Part: Instead of just guessing the rules, the system reads thousands of scientific papers (specifically titles and abstracts) about the specific microbes involved. It turns these words into a "digital summary" (text embeddings).
The "Adaptive" Part: The system combines the video footage (abundance data) with the library summaries (text knowledge) to create a custom set of rules for that specific moment. It asks: "Based on what we see and what we know from the books, how should these microbes interact right now?"

3. The Engine: A2G2 (The Brain)

To make this work, they built a specific type of AI brain called A2G2. Think of it as a three-part machine:

The Listener (Feature Encoder): It listens to three different voices at once: the raw numbers of who is there, some statistical summaries, and the "voice" of the scientific literature. It uses a special "attention" mechanism to decide which voice is most important for the current prediction.
The Mapmaker (Structural Encoder): Microbes don't interact in a straight line; they form a complex web. This part builds a map of who is connected to whom, but it does it efficiently so it doesn't get overwhelmed by too many connections.
The Translator (Reconstruction Head): It takes the complex map and the combined knowledge and translates it back into the mathematical rules (growth rates and interaction strengths) that the gLV equation needs.

4. The Results: Smarter Predictions

The authors tested this on real-world data from human guts and ginger plant roots.

Without Knowledge: Even without reading the books, their new model was already 53% better at predicting microbial behavior than the previous best methods. It was like having a detective with better eyesight.
With Knowledge: When they added the scientific literature into the mix, the model got even smarter. It improved accuracy by up to 23% and made the mathematical fit 47% better.
The "Unseen" Test: They tested if the model could guess how a microbe it had never seen before would behave. By using the text descriptions of that microbe, the model could generalize and make good predictions, proving that the "reading" part helped it understand new characters.

5. What They Discovered (The "Aha!" Moments)

By looking at the rules the model learned, they found biological patterns that matched real-world science:

In Human Guts: They found that a family of bacteria called Bacteroidaceae acts like a "keystone" (a central pillar holding the ecosystem together), just as scientists had suspected from years of research.
In Ginger Roots: They identified specific bacteria that act as "hubs" or leaders, supporting or competing with others in ways that matched previous studies on soil health.

Summary

In short, this paper presents a new tool that doesn't just crunch numbers; it reads the library. By combining hard data (what we see) with soft knowledge (what we know from books), it creates a much more accurate and reliable map of how microscopic communities live, fight, and cooperate. It proves that in science, knowing the history of the players helps you predict the game much better than just watching the score.

Technical Summary: Knowledge-Inclusive Adaptive Physics-Informed Neural Network for Microbial Interaction Modelling

1. Problem Statement

Microbial interaction modelling is critical for understanding ecosystem function, host health, and biotechnological applications. However, characterizing these interactions remains a fundamental challenge. Microbial dynamics are governed by internal pairwise interactions and external environmental influences (e.g., temperature, nutrients). While the Generalised Lotka-Volterra (gLV) equation serves as the standard biological foundation for modelling these dynamics, existing approaches face significant limitations:

Data Limitations: Current methods rely solely on experimental abundance measurements, which capture only a narrow slice of system behavior under specific conditions, failing to account for broader contextual variations.
Knowledge Gap: Existing Physics-Informed Neural Networks (PINNs) for parameter discovery learn equation parameters strictly from data, ignoring the vast heterogeneous knowledge (text, network structures) accumulated in scientific literature and databases.
Architectural Deficiencies: Previous methods often fail to simultaneously capture temporal dynamics, interaction topology, and contextual knowledge. LSTM-based approaches lack topological grounding, while Graph Neural Network (GNN) approaches often lack temporal representation. Furthermore, existing gLV-based methods estimate parameters from abundance data alone, ignoring context-aware knowledge that could improve reliability.

2. Methodology: KI-APINN and A2G2

The authors propose Knowledge-Inclusive Adaptive Physics-Informed Neural Networks (KI-APINN), a model-agnostic framework that conditions physics equation parameters on a "knowledge-inclusive" representation formed by fusing experimental data with auxiliary knowledge sources.

2.1 Framework Overview

Unlike standard Adaptive PINNs (APINNs) where parameters are fixed scalars or learned solely from data, KI-APINN learns parameters as functions of a fused representation ( $z$ ). This representation integrates:

Experimental Inputs: Microbial abundance profiles.
Derived Data: Statistical parameters and taxonomic richness.
Contextual Knowledge: Text embeddings from peer-reviewed metagenomics literature (titles and abstracts) and network structural knowledge.

The framework minimizes a composite loss function comprising a data term ( $L_{Data}$ ) and a physics term ( $L_{Physics}$ ), where the physics parameters ( $\theta$ ) are dynamically generated by a parameter network ( $\theta_\psi$ ) based on the knowledge-inclusive representation $z$ .

2.2 A2G2 Architecture

To instantiate KI-APINN for microbiology, the authors developed A2G2, a specific neural architecture comprising three components:

Attention-Based Feature Encoder: Fuses temporal abundance profiles (processed via Gated Recurrent Units), statistical parameters, taxonomic richness, and text embeddings. It employs a per-modality attention mechanism to weigh the contribution of each knowledge source, providing interpretability.
Structural Encoder (AnchorGNN): A novel sparse graph encoding mechanism designed to capture microbial interaction topology at sub-quadratic cost. It sparsifies the interaction graph by learning a set of "anchor taxa" and retaining edges only incident to these anchors, reducing computational complexity from $O(n^2)$ to $O(nk)$.
gLV Reconstruction Head: Decodes the learned representations into per-taxon growth rates ( $r_v$ ) and pairwise interaction strengths ( $B_{vu}$ ), effectively closing the loop between the neural architecture and the gLV physics equation.

2.3 Pipelines

The study evaluates two distinct pipelines:

Mono-Community Pipeline: Focuses on a single microbial community, allowing for the integration of community-specific internal and external factors.
Multi-Community Generalisation Pipeline: Models interactions across multiple communities simultaneously to capture shared dynamics and generalise to unseen taxa.

3. Key Contributions

KI-APINN Framework: A generalisation of parameter-discovery PINNs that conditions physics parameters on learned knowledge-inclusive representations, recovering standard PINNs as a special case when no auxiliary knowledge is present.
A2G2 Architecture: A concrete instantiation combining multimodal attention fusion, anchor-based sparse graph encoding, and gLV-grounded parameter decoding.
Comprehensive Evaluation: The most extensive evaluation in this domain to date, covering six datasets (human gut, ginger rhizosphere, in vitro, simulated, and neonatal) across both mono- and multi-community pipelines.
Biological Insights: Validation of inferred interaction networks against established biological knowledge (MetagenomicKG), revealing keystone species and context-dependent interaction patterns.

4. Results

The framework was evaluated using Bray-Curtis Dissimilarity (BCD) based accuracy and $R^2$ scores.

Performance vs. State-of-the-Art: Even without auxiliary knowledge, the A2G2 model improved over the state-of-the-art (IMPARO and LSTM baselines) by up to 53% in BCD accuracy.
Impact of Knowledge Integration:
- Gut Microbiomes: Text integration consistently improved modelling. In the mono-community pipeline, adding text yielded gains of up to 23% in BCD accuracy and 47% in $R^2$ .
- Ginger Rhizosphere: Benefits were treatment-dependent, with the strongest improvements (up to 23% BCD, 47% $R^2$ ) observed under specific dilution treatments (BV138 200×).
- Unseen Taxa: In the multi-community pipeline, text guidance enabled robust generalisation to unseen taxa, improving performance by 1.3–2% in BCD and 4.0–4.4% in $R^2$ across 25 unseen species.
- Neonatal Microbiomes: Text integration showed mixed results, with benefits observed in gut samples but minimal response in respiratory microbiomes (throat/nasal), suggesting domain-specific applicability of literature knowledge.
Knowledge Graph Integration: Adding structured Knowledge Graph (KG) edge embeddings provided consistent gains (up to 19% BCD and 47% $R^2$ ) when combined with text, outperforming unstructured text alone in some configurations.
Network Analysis: The inferred networks identified biologically plausible keystone species (e.g., Bacteroidaceae in male gut, Xanthomonadaceae in ginger rhizosphere) and interaction patterns consistent with literature, such as cross-feeding and cooperative networks.

5. Significance and Claims

The paper claims that KI-APINN addresses a critical gap between the narrow scope of experimental data and the broad contextual understanding encoded in scientific literature. By integrating heterogeneous knowledge sources (text and network structure) into physics-informed learning, the framework:

Enhances Parameter Discovery: Moves beyond data-driven parameter estimation to context-aware inference, improving accuracy and stability, particularly in complex ecosystems like the rhizosphere where simple gLV dynamics may be insufficient.
Provides Interpretability: The attention mechanism and explicit gLV parameter output allow researchers to understand which knowledge sources drive predictions and to interpret microbial interaction strengths.
Offers Generalisability: The framework demonstrates the ability to generalise to unseen taxa and diverse ecological contexts (human, plant, synthetic), suggesting a path toward more robust and transferable microbial community models.

The authors conclude that while the gLV equation is not a universal description of all microbial dynamics, conditioning its parameters on knowledge-inclusive representations allows the model to remain faithful to known biological structures while adapting to context-dependent dynamics that equations alone cannot capture.