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NUCLEUS-MoE: Unified Model of Pool Boiling for Liquid Cooling

NUCLEUS-MoE is a unified mixture-of-experts model that leverages neighborhood attention and signed distance fields to accurately simulate diverse pool boiling dynamics across multiple fluid classes, achieving superior generalization and physical consistency compared to existing specialized surrogates.

Original authors: Arthur Feeney, Xianwei Zou, Sheikh Md Shakeel Hassan, Siddhartha Rachabathuni, Aparna Chandramowlishwaran

Published 2026-05-28

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arthur Feeney, Xianwei Zou, Sheikh Md Shakeel Hassan, Siddhartha Rachabathuni, Aparna Chandramowlishwaran

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

The Big Problem: Boiling is Chaotic and Hard to Predict

Imagine you are trying to predict how water boils in a pot. It's not just water turning to steam; it's a wild dance of bubbles forming, rising, popping, and swirling. Sometimes the water is already hot (saturated boiling), and sometimes it's cold, causing bubbles to shrink as they rise (subcooled boiling).

Scientists have known for a long time that boiling is the most efficient way to cool things down (like super-hot computer chips). But predicting exactly how it happens is a nightmare for computers.

The Old Way: Scientists used to run massive, slow simulations for every single type of liquid and every single temperature. It was like hiring a different chef for every specific recipe you wanted to cook.
The Problem: If you tried to teach one computer model to handle all liquids (from freezing liquid nitrogen to hot refrigerants) and all boiling types, it would get confused. It would start "hallucinating," mixing up the rules (like thinking a cold bubble should grow in hot water).

The Solution: NUCLEUS (The "Swiss Army Knife" Chef)

The researchers built a new AI model called NUCLEUS. Think of it not as a single chef, but as a team of specialized chefs working in one kitchen, managed by a smart head chef.

This team uses a technique called Mixture of Experts (MoE). Here is how it works:

The "Head Chef" (The Router): When the model sees a part of the boiling pot, the router looks at it and asks, "What is happening here?"
- If it sees a bubble rising in hot liquid, it sends that task to Expert A (the "Hot Bubble Specialist").
- If it sees a bubble shrinking in cold liquid, it sends that task to Expert B (the "Cold Condensation Specialist").
- If it sees a wall getting hot, it sends it to Expert C (the "Heat Transfer Specialist").
The "Specialists" (The Experts): Each expert is a small AI brain that only knows how to handle one specific type of physics. They don't try to do everything. This prevents the model from getting confused when the rules change (like switching from hot water to liquid nitrogen).
The Result: The model learns to "unify" all these different boiling scenarios into one single system. It doesn't need a different model for every fluid; it just routes the problem to the right expert.

The Secret Ingredients

To make this work, the researchers added three special "ingredients" to the recipe:

Neighborhood Attention (The "Local Gossip"):
In boiling, what happens in the top-left corner of the pot doesn't affect the bottom-right corner right now. The physics is local.
- Analogy: Imagine a crowded room. You only really need to listen to the people standing next to you to understand the conversation. You don't need to hear everyone in the building.
- The Fix: NUCLEUS only looks at its immediate neighbors. This makes it faster and more accurate because it stops trying to connect dots that aren't connected.
Signed Distance Field Reinitialization (The "Reality Check"):
The model tracks the shape of the bubbles using a mathematical map. Over time, as the model predicts step-by-step, this map can get "wobbly" or distorted, like a rubber band stretching too far.
- The Fix: The model has a built-in "reality check" (called Sussman reinitialization) that constantly snaps the bubble shapes back to their correct, smooth forms. This stops the bubbles from turning into weird, glitchy waves over time.
The "Zero-Shot" Talent (Learning by Analogy):
The model was trained on three types of fluids: dielectrics, refrigerants, and cryogens (like liquid nitrogen).
- The Test: The researchers then gave it a brand-new fluid it had never seen before (Opteon 2P50).
- The Result: Because the model learned the underlying rules of boiling rather than just memorizing specific fluids, it could figure out how to handle this new fluid with very little extra training. It was like a chef who knows how to cook steak perfectly and can immediately figure out how to cook a new type of fish without a recipe.

Why This Matters

Speed: The new model is about 4 times faster and uses 3 times less computer memory than previous models.
Accuracy: It doesn't just guess the average temperature; it predicts the exact movement of bubbles and heat, matching high-speed physics simulations.
Unification: It is the first model to successfully handle both "hot boiling" and "cold boiling" across extreme fluids in a single architecture.

Summary

The paper presents NUCLEUS, a smart AI that acts like a team of specialized experts. Instead of trying to be one giant brain that knows everything about boiling (which leads to confusion), it routes different parts of the problem to the right specialist. This allows it to predict how different liquids boil, from freezing cold to scorching hot, with high speed and accuracy, all within a single system.

Technical Summary: NUCLEUS-MoE: Unified Model of Pool Boiling for Liquid Cooling

Problem Statement

Pool boiling is a highly efficient heat transfer mechanism essential for emerging technologies like data-center thermal management and nuclear energy systems. However, modeling boiling dynamics is computationally prohibitive due to the strong coupling between phase change, turbulence, and transport, as well as extreme sensitivity to fluid properties and thermodynamic conditions.

Existing learning-based surrogates face significant limitations:

Lack of Unification: Current models are typically trained separately for specific fluids or conditions (e.g., saturated vs. subcooled boiling). Attempts to train unified models often fail, exhibiting "leakage" where phenomena from one regime (e.g., condensation) erroneously appear in another (e.g., saturated boiling).
Generalization Failure: Standard conditioning methods (e.g., FiLM) struggle to handle the discrete reversals in phase-change physics and extreme variations in thermophysical properties across different fluids (e.g., dielectrics vs. cryogens like liquid nitrogen).
Physical Inconsistency: Models often fail to maintain interface consistency over long autoregressive rollouts, leading to error accumulation and unphysical dynamics.

Methodology: NUCLEUS Architecture

The authors propose NUCLEUS, a single mixture-of-experts (MoE) architecture designed to unify saturated and subcooled boiling across multiple fluid classes (dielectrics, refrigerants, and cryogens). The model is trained on high-fidelity Flash-X simulations from the BubbleML dataset.

The architecture integrates three physics-informed components:

1. Neighborhood Attention

Boiling transport is governed by local interactions; the state at a specific location depends primarily on a bounded neighborhood determined by fluid velocities and diffusion rates.

Mechanism: Instead of using global attention (e.g., ViT) or axial attention, NUCLEUS employs neighborhood attention, restricting each spatial query to attend only to keys within a fixed radius.
Rationale: This encodes the inductive bias of finite domains of influence, reduces computational cost for high-resolution data, and aligns with the physical reality that distant regions do not influence local dynamics over short time intervals.

2. Mixture-of-Experts (MoE) Routing

The core challenge is the heterogeneity of boiling physics: saturated boiling involves evaporation at the heater, while subcooled boiling involves bulk condensation. These represent fundamentally different operators for energy transport.

Mechanism: Dense MLP layers are replaced with sparse MoE layers (8 experts, top-2 routing). A learned router directs input patches to specific experts based on the local physical context.
Emergent Specialization: Without explicit supervision, the model learns to decompose the problem. Experts naturally specialize in distinct physical phenomena (e.g., some experts track rising bubbles and high-temperature regions, while others handle bulk liquid or thermal boundary layers). This allows the model to learn separate approximate operators for evaporation-dominated vs. condensation-dominated transport within a unified backbone.

3. Signed Distance Field (SDF) Reinitialization

Autoregressive inference often causes the signed distance function ( $\phi$ ), which tracks the phase boundary, to drift from the Eikonal equation ( $||\nabla \phi||^2 = 1$ ), particularly in regions far from the interface.

Mechanism: The authors apply the Sussman method to reinitialize the SDF during inference. This iterative scheme solves a partial differential equation to restore the distance property using the zero level set (the predicted interface) as a boundary condition.
Impact: This test-time correction prevents error accumulation and spurious "wave" artifacts, ensuring interface consistency over long rollouts.

Key Contributions

Unified Surrogate Model: NUCLEUS is the first architecture to successfully learn a single model for both saturated and subcooled pool boiling across multiple fluids with widely varying thermophysical properties, eliminating the need for separate specialized models.
Physics-Informed Design: The integration of neighborhood attention, MoE routing, and SDF reinitialization directly addresses the specific physical challenges of multiphase transport, interface motion, and local interactions.
Interpretability: The paper demonstrates that expert routing exhibits coherent spatial structure and emergent specialization to physical phenomena without explicit supervision, providing insight into how the model decomposes heterogeneous boiling dynamics.
State-of-the-Art Performance: NUCLEUS matches or exceeds the accuracy of baselines (including Bubbleformer, MoE-DPOT, and Poseidon) while maintaining physical consistency over long rollouts.
Generalization Capability: The model demonstrates zero-shot and few-shot generalization to a new fluid (Opteon 2P50) unseen during pretraining, requiring only minimal fine-tuning.

Experimental Results

The model was evaluated on the BubbleML dataset covering three fluids (FC-72, R515B, LN2) and two boiling regimes.

Accuracy: NUCLEUS achieved the lowest Mean Absolute Error (MAE) across all fields (temperature, velocity, SDF) compared to baselines. Notably, it significantly outperformed Bubbleformer on the unified dataset, which suffered catastrophic failures due to physics leakage.
Stability: In long-horizon autoregressive rollouts, NUCLEUS preserved the distributional statistics of temperature and vertical velocity (measured via Earth Mover's Distance) much better than dense MLP baselines, which exhibited systematic drift and underestimated bubble-induced mixing.
Efficiency: Leveraging neighborhood attention and MoE sparsity, NUCLEUS is approximately 4 $\times$ faster and requires 3 $\times$ less memory than comparable dense MLP baselines. At high resolutions (2048 $\times$ 2048), it is 5–6 $\times$ faster than full attention transformers.
Few-Shot Transfer: When fine-tuned on only three simulations of a new fluid (Opteon 2P50), NUCLEUS converged substantially faster and achieved lower errors than training a model from scratch on the same limited data.

Significance and Claims

The paper claims that NUCLEUS establishes a scalable pathway toward unified surrogate modeling of boiling dynamics. By demonstrating that MoE architectures can naturally align with the heterogeneous nature of scientific physics—separating distinct regimes while preserving shared representations—the work lays the groundwork for broader generalization in scientific machine learning.

The authors position NUCLEUS not merely as a faster simulator, but as a foundation model capable of acting as a base for multi-phase, multi-physics modeling. The successful unification of saturated and subcooled boiling across extreme fluids (including cryogens) addresses a critical gap in current thermal management modeling, enabling more robust design exploration for high-performance liquid cooling systems.