WarpStack — Hybrid Numerical + AI Warpage Analysis for 2.5D/3D Chiplets

Why it matters

When the package bends, reliability breaks

Stacking silicon, interposers, and memory bonds materials with very different expansion rates. As the assembly heats and cools, those mismatches make the whole package bow and twist — and that warpage is a first-order reliability risk in modern 2.5D and 3D integration.

🌡️

Heat makes it move

Every material in the stack expands by a different amount. Cycle the package from assembly to operating temperature and those mismatches build internal stress that warps the whole structure.

⚠️

Warpage causes failures

Too much bow leads to cracked dies, delaminated layers, and open solder joints — and it makes assembly yield fall. Catching it early is far cheaper than finding it on the line.

🔁

It has to be checked often

Floorplanning, stack-up choices, and material selection all change how a package warps. Designers need a warpage answer on every iteration — not once, at the very end.

Why a few microns matter. As the assembly cools from bonding to operating temperature, mismatched expansion bows the package into a convex (∩) or concave (∪) shape. Where the gap opens too far the solder bump pulls apart into an open circuit; where it closes too far, neighboring bumps merge into a short. WarpStack predicts that bow — and where it peaks — so these failures are caught in design, not on the assembly line.

What it does

Three methods, one workflow — numerical and AI

WarpStack is a hybrid engine: a fast 2D numerical method for screening, a detailed 3D numerical method for accurate sign-off, and WarpStack-AI (GNN) — an AI-accelerated method for near-instant, numerical-grade warpage. All three run from the same simple design description, so you move between speed, accuracy, and real-time inference without changing your inputs.

FAST · NUMERICAL

⚡ 2D numerical screening in a blink

The fast 2D numerical returns a full warpage map in about a third of a second — the same speed whether the design has 3 layers or 11. Sweep hundreds of floorplans and stack-ups without waiting.

ACCURATE · NUMERICAL

🎯 3D numerical for the hard cases

The detailed 3D numerical resolves the package through its full thickness, layer by layer — the fidelity you want for complex, interleaved multi-layer stacks where a fast estimate isn't enough.

REAL-TIME · AI

🧠 WarpStack-AI (GNN) inference

An AI-accelerated method, trained on numerical ground truth, predicts full warpage maps in ~1.5 ms at ~1% error — fast enough to put warpage inside a live optimization loop, and it generalizes to designs it has never seen.

SCOPE

🧱 Real multi-layer stacks

Handles arbitrary layer stacks — substrates, interposers, bumps, dies, spreaders, lids — with per-layer materials and per-die placement. Validated on designs from 3 to 11 layers and 10 to 18 dies.

MAPS

🗺️ Clear, visual output

Every run produces warpage heatmaps, cross-sections, and a 3D stack view, plus the peak-to-peak bow in microns — so the shape and the number are both easy to read.

COMPARE

⚖️ 2D vs 3D, side by side

A built-in compare mode runs both solvers and shows exactly where they agree and where they differ — so you know which designs the fast 2D can screen and which ones truly need 3D.

SCRIPTABLE

🔭 Batched & automatable

A command-line interface and structured JSON in, CSV/JSON out make WarpStack easy to script — run one design or a whole batch, and feed the results straight into your own design flow.

STANDARDS · INPUT

🧩 Speaks IEEE 3Dblox

Import designs described in IEEE 3Dblox — the IEEE-standard modular description language for physical stacking, dimensions, and logical connectivity in 2.5D and 3D-IC designs. Bring your stack straight from the ecosystem, no hand re-entry.

Workflow · agentic integration

Built for agentic EDA flows

WarpStack is designed to drop straight into agentic EDA and system-design workflows. A first-class CLI and structured data interface let autonomous design agents call fast 2D numerical, detailed 3D numerical, or WarpStack-AI (GNN) inference, read back machine-readable warpage maps and peak-to-peak margins, and feed them into floorplanning, stack-up, and material-selection loops — for warpage-aware optimization and warpage reliability sign-off of chiplets and advanced packages in system design. With millisecond AI inference, warpage finally runs at the speed of the loop itself.

Agentic-flow ready — built to be driven by autonomous EDA and system-design agents, and to plug into any agentic flow.
CLI-first — every warpage analysis is scriptable from the command line; nothing in the loop needs a GUI.
Structured data interface — machine-readable floorplans in; warpage surfaces, peak-to-peak bow, and signed 3D−2D difference maps out, ready for closed-loop automation.
Warpage-aware optimization — at ~1.5 ms per evaluation, WarpStack-AI (GNN) lets agents sweep thousands of floorplans, stack-ups, and materials in a live loop, steering each candidate toward lower bow in real time.
Reliability sign-off — AI or fast 2D screens the whole design space; detailed 3D numerical signs off the critical chiplet and advanced-package designs against warpage limits before tape-out and assembly.

agentic-flow ready CLI-first structured data interface IEEE 3Dblox input AI-accelerated warpage-aware optimization reliability sign-off

Closed-loop warpage optimization

◆ Agentic EDA / system-design flow

An autonomous agent drives floorplan, stack-up, and material decisions for the chiplet or advanced package.

↓ invokes WarpStack — CLI + structured data interface

▣ WarpStack warpage analysis

WarpStack-AI (GNN) inference, fast 2D numerical, or detailed 3D numerical runs headless, producing warpage maps and peak-to-peak margins directly for automation.

↓ returns structured, machine-readable results

↻ Fed back to the agent

Warpage hotspots, peak-to-peak bow, and reliability margins steer the next floorplan, stack, or material iteration automatically.

Warpage analysis becomes a callable step inside your agentic flow — not a hand-run GUI task.

How it works

From one floorplan to a warpage map

You describe the package once — its layers, materials, and where each die sits. WarpStack builds a mechanical model of the stack, applies the thermal load, and solves for how the surface deflects. Then pick the method that fits the moment: fast 2D numerical, detailed 3D numerical, or WarpStack-AI (GNN) inference. The inputs are identical.

Describe the package

A single structured file lists the layer stack, each layer's material, and the placement of every die or module — the whole design in one place. WarpStack also reads IEEE 3Dblox, the standard modular description language for 2.5D/3D-IC stacking and connectivity, so you can bring designs straight from the ecosystem.

Apply the thermal load

WarpStack takes the package from its stress-free assembly temperature down to operating temperature, so the expansion mismatches between layers turn into real bending.

Solve — or predict — the shape

A numerical solver computes how the surface deflects — a fast 2D method for screening, a detailed 3D method for sign-off. Or skip the solve entirely and let WarpStack-AI (GNN) — an AI-accelerated method trained on that same numerical output — predict the warpage map in milliseconds.

Read the result

Out come warpage heatmaps, cross-sections, and the peak-to-peak bow in microns — identical format from every method, ready to view, compare, or drop into your own scripts.

2D numerical

numerical · fast · screening

A fast numerical method that solves the bow on a plane — the lowest-cost estimate, ideal for sweeping many designs.

~0.35 s
per design3–11
layers

3D numerical

numerical · detailed · sign-off

A detailed numerical method that resolves the package through its full thickness — the ground-truth fidelity for complex, interleaved stacks.

9 s–8 min
per designfull
3D field

WarpStack-AI (GNN)

AI · real-time · in-the-loop

An AI-accelerated method, trained on numerical ground truth, that predicts the full warpage map directly — no solve required.

~1.5 ms
per design~1%
error vs numerical

Numerical for truth, AI for speed

The three methods are built to work together. Screen the whole space with the fast 2D method, sign off the critical designs with the detailed 3D method, and — once WarpStack-AI (GNN) is trained on that numerical output — call the AI for near-instant maps whenever you need warpage inside a live loop. Because the AI learns from the same numerical engine that validates it, you get numerical-grade answers at AI speed. Same floorplan, same materials — you simply choose truth, detail, or speed.

2D numerical screening 3D numerical sign-off AI-accelerated trained on numerical data generalizes to unseen designs CLI & structured data IEEE 3Dblox input

Warpage is reported as peak-to-peak deflection in microns with the full surface map — in the same format from the numerical methods and from the AI.

Results

Fast where you can, accurate where you must, instant when it counts

First, the numerical engine on a batch of nine 2.5D and 3D benchmark designs — fast 2D numerical and detailed 3D numerical, from a 3-layer module to an 11-layer chiplet. Then WarpStack-AI (GNN), benchmarked against numerical ground truth: numerical-grade warpage in milliseconds, even on designs it has never seen.

Fast 2D — screen every design in under a second

2D solve time by design

One floorplan → one warpage map

~0.35 s each

Design	Layers	Dies	2D time
3-layer module	3	12	0.342 s
Planar 16-die array	3	16	0.347 s
Arbitrary-layer module	5	12	0.345 s
GaAs RF PA array	5	15	0.347 s
HBM3 memory stack	6	10	0.346 s
5 nm CPU	7	18	0.347 s
2.5D chiplet	9	14	0.347 s
11-layer 3D chiplet	11	16	0.356 s

Package sizes here span 5 mm to 200 mm on a side. The 2D solve time barely moves — every design lands between 0.34 s and 0.36 s, regardless of layer count, die count, or package size.

From stack to warpage

cores_16_1 · 16-die planar array

2D result

3D structure view of the cores_16_1 design — 16 die tiles arranged on a large planar substrate — **The design.** 16 dies on a 200 mm, 3-layer planar substrate — the 3D structure WarpStack builds from the floorplan.

2D warpage map of a large 16-die planar array — a strong central dome reaching about 1465 microns peak-to-peak — **Its 2D warpage.** That large, low-layer package bows into a pronounced dome — about **1465 µm** peak-to-peak — solved in 0.35 s.

Detailed 3D — layer-specific warpage the flat model can't see

Same design, three surfaces — HBM3 memory stack

A 6-layer, 10-die DRAM stack on a 12 mm interposer

2D vs 3D

The fast 2D method returns a single, smooth package bow. The 3D method resolves the stack layer by layer, so it reports warpage per surface — the die-level active surface and the continuous package surface — capturing local, die-specific deflection that the flat 2D map averages away.

3D structure view of the HBM3 stack — stacked DRAM dies on an interposer beneath an overmold encapsulant — Design · 3D structureThe stack. 6 layers — interposer, micro-bumps, three DRAM tiers, and overmold — with 10 dies.

2D warpage map of the HBM3 stack — a single smooth central bowl with no per-die structure — Fast 2D · screening2D numerical result. One smooth bowl, ~10 µm peak-to-peak — a fast, whole-package estimate with the stack collapsed to a plane.

3D active-surface warpage map of the HBM3 stack showing each DRAM die deflecting individually within its outline — Detailed 3D · die surface3D active surface. Each DRAM die now bends on its own — the local, die-specific warpage that matters for cracking and bond reliability.

3D package-surface warpage map of the HBM3 stack — the continuous encapsulant top surface bowing — Detailed 3D · package surface3D package surface. The continuous encapsulant top — the global package bow, reported separately from the die-level view.

Because the 3D solver models every layer through its thickness, it doesn't just give a more accurate number — it tells you where the warpage lives. The die-level active surface and the package-level surface come out as separate maps, so you can see local die deflection and the overall package bow independently. The flat 2D method, by design, blends all of that into a single averaged surface.

2D vs 3D — where fast is already close enough

Closest-agreement designs

Peak-to-peak warpage, 2D vs 3D

2D within ~10–20%

Design	2D	3D	Agreement
Arbitrary-layer module 5L	251 µm	269 µm	93%
2.5D chiplet 9L	50 µm	44 µm	88%
Planar 16-die array 3L	1465 µm	1256 µm	86%
HBM3 memory stack 6L	10.1 µm	8.3 µm	83%
16-die array, variant 3L	1696 µm	1370 µm	81%

For these designs the fast 2D map already predicts the 3D peak warpage within roughly 10–20% — close enough to screen and rank candidates before committing to a full 3D run. Deep, interleaved stacks (like the 11-layer chiplet) diverge more — exactly the cases where the 3D analysis earns its extra time.

How much faster 2D runs

3D solve time ÷ 2D solve time

up to 1400×

11-layer 3D chiplet

1411×

2.5D chiplet

285×

5 nm CPU

153×

GaAs RF PA array

57×

HBM3 memory stack

33×

3-layer module

26×

The 3D solve grows with the size and depth of the stack — from about 9 s for a simple module to roughly 8 minutes for the 11-layer chiplet. The 2D solve stays near 0.35 s throughout, so the speed gap widens exactly where design-space exploration needs it most.

WarpStack-AI (GNN) — numerical-grade warpage in milliseconds

AI inference vs numerical solve

Per-design runtime and accuracy

up to 120,000×

Method	Runtime	vs 3D numerical	Error vs numerical
3D numerical reference	174.5 s	1×	—
2D numerical screening	~0.35 s	~500×	est.
WarpStack-AI GNN	1.46 ms	119,766×	1.26%

WarpStack-AI (GNN) returns a full warpage map in 1.46 ms — about 120,000× faster than a 3D numerical reference and ~200× faster than the fast 2D numerical method — at 1.26% normalized RMSE and 2.21% peak-warpage error against numerical ground truth. It also trains efficiently: ~33 minutes, roughly 70% less training time than a comparable AI baseline at equal accuracy.

Generalizes to unseen designs

Held-out design families, never seen in training

≤ 3.7% RMSE

Unseen dataset	Norm. RMSE	Norm. MAE
Case ①	2.32%	1.78%
Case ②	2.62%	1.86%
Case ③	3.01%	2.31%
Case ④	3.69%	2.68%

Point the trained network at floorplans and stack-ups it never saw and the accuracy holds — at most 3.69% normalized RMSE across four held-out design families, at the same millisecond runtime. Accurate enough to keep warpage inside an early-stage optimization loop on brand-new designs, without retraining.

WarpStack-AI (GNN) is an AI-accelerated warpage predictor trained on numerical ground truth. Because it learns from the same numerical engine that validates it, the numerical and AI paths stay consistent — so you get numerical-grade warpage maps at AI speed.

See how your chiplet stack bends — before it ships.