Explain the residual before adding variables
Scale, background, cell, profile and coordinates all influence a diffraction pattern. Opening them in stages lets each trial test a smaller hypothesis, reducing ambiguity from correlated adjustments.
Sage-A1.5 / CRYSTALASSAYER
Autonomous Rietveld Refinement
Three roles turn diffraction feedback into the next parameter choice: plan a trial, run numerical optimization and review the result. Follow the fit improving step by step.
8 trials. Rwp: 88.3091% → 86.1092%.Sc₂Au₆ · Recorded experiment · Total decrease: 2.1999 percentage points
Sc2Au6CRYSTAL / 005
01 / CRYSTAL STRUCTURESc · Au02 / DIFFRACTIONObservedCalculated
Rwp88.3091%Initial state · 00 / 08
RECORDED REFINEMENT / CASE 005
From the observed pattern to the next decision
Follow successive updates to the background, cell and atomic coordinates, guided by the pattern residual.
Sc₂Au₆CASE 005 · 8 ATOMS
Sage-A1.5 · 2026.09.18
Sage-A1.5 · 2026.09.18
Sc₂Au₆ / Initial cell
ScAuWireframe: unit cell
WebGL is unavailable. The Rwp curve and trial records remain available.
Observed and current calculated patterns
PATTERN → RESIDUALObservedCalculatedObserved − calculated
Weighted pattern residual → Rwp
Weighted profile residual · Rwp
INITIAL CHECKPOINT88.3091%Initial state
Points are accepted checkpoints after each trial. Connecting lines are replay guides, not inner solver steps. Orange points indicate rejected trials.
Initial state · awaiting a plan
PLANNER → EXECUTOR → REVIEWER → CHECKPOINTSESSION / INITIALIZED00 / 04
00 / 0800:00 / 01:36
Initial → final Rwp88.3091 → 86.1092%
Total decrease / percentage points2.1999 pp
Outer trials / max inner steps8 trials / 20 steps
State updated / previous state kept6 updates / 2 retained
01 / DECISION TRACE
Why optimize these parameters now?
The Planner proposes a hypothesis, the Executor runs a bounded trial, and the Reviewer checks the result. The numerical gate controls the accepted state.
Load the initial structure and observed pattern
Initial state01 · PLANNER
02 · EXECUTOR
03 · REVIEW + GATE
Original role outputs and solver termination
02 / PARAMETER CHANGES
From parameter changes to the pattern residual
Scale and background affect overall intensity; the cell affects reflection positions; coordinates affect structure factors. Each trial opens only its selected block.
The current structure and pattern share the same accepted parameters. Structure factors produce a calculated pattern, whose difference from the observed pattern is weighted by the standard deviation to obtain Rwp.
Observed data come from the original XYE. Calculated patterns are replayed with the frozen forward model on CPU float64. Rwp values always come from the original NPU run.
| Parameter | Initial | Current accepted |
|---|
Atom indices start at 0; atom.0 is fixed throughout. Coordinate displacement uses the initial lattice and excludes motion due to cell changes. This case did not open zero or profile.
03 / WHY A CLOSED LOOP
Refinement needs a solver and decisions
Numerical optimization determines how to update a chosen block. The loop also decides which variables to open, when to continue and which results to retain.
Reallocate trials after stagnation
This run adjusts cell lengths and then tests angles. The angle improvement is too small, so the loop retains the previous state and turns to coordinates. When a repeated block stalls, it moves to other atoms.
Suggestions can fail; state updates stay controlled
In trial 5, the Reviewer suggests acceptance, but Rwp rises by about 1.10×10⁻⁸ percentage points. The numerical gate blocks the suggestion and retains the trial-4 checkpoint, producing a plateau.
Acceptance requires valid physical constraints, a sufficient Rwp decrease and Reviewer approval. The Reviewer may also reject a numerically eligible trial. Every new trial starts from the last accepted checkpoint.
04 / RECORDED TRAJECTORY
Eight trials, each with a record
| Trial | Parameter block | Trial Rwp / % | Accepted Rwp / % | State decision |
|---|
Trial 3 reduced Rwp by approximately 0.000289 pp but was rejected by the Reviewer. Trial 5 was blocked by the numerical gate. Neither changed the accepted structure.