The network learns arrows.
At each state, it predicts the direction and speed of change. It does not simply memorise a list of future positions.
A CAPSTONE YOU CAN PLAY WITH
A world of
complexity.
A handful
of patterns.
Can we teach a small model to capture a changing atmosphere? Step inside a year of experiments with patterns, physics and machine learning.
View the poster ↗No background in climate science needed. Just curiosity.
A REAL PATTERN. A SMALLER WORLD.
Temperature pattern · Mode 01500 hPa
Millions of values.41 changing strengths.
2,867,040values in one atmospheric snapshot
→
41retained patterns to work with
×
14,976daily snapshots · 1984–2024
Meet the project ↗
01 / FIND THE PATTERNS
First, listen to
the orchestra.
A whole orchestra makes a complicated sound. But you can describe the mix using a few familiar parts, and how strongly each part is playing.
THE MIXING DESKTeaching analogy
Low patternMiddle patternHigh pattern→ The combined signal
You're the conductor.
Move the faders. The patterns stay the same; their strengths change.
Faders blend bass, chords and a soft melody. The waves are a schematic of adding patterns.
HERE IS THE CONNECTION
The pattern stays fixed.
Its strength changes.
In the orchestra, a part gets louder or quieter. In POD, each part is a map: its coefficient turns the whole pattern up, down, or reverses its sign. Add the contributions to build an atmospheric anomaly map.
FIXED PATTERN 01
+
× —strength on 15 January 2024
FIXED PATTERN 02
+
× —strength on 15 January 2024
FIXED PATTERN 03
=
× —strength on 15 January 2024
THEIR COMBINED CONTRIBUTION
One anomaly mapMore modes add more spatial information.
The thumbnails are real supplied patterns, shown at one typical coefficient amplitude. The multipliers are observed strengths in those same units. All four maps use the same colour scale; these three modes are only part of the retained reconstruction.
AT ANY TIMEanomaly = Σ (fixed pattern × changing strength)
Show me the formal POD equation
X̂′(r, t) = ∑i=1R ai(t)
φi(r)
Here, r denotes location, while R is the number of retained modes. Each φi is a fixed spatial pattern. Its coefficient ai(t) changes with time. This equation reconstructs anomalies only. In this project we have 41 supplied patterns, each spanning wind, temperature and humidity. POD finds the patterns and observed strengths; the dynamical model must learn how the strengths evolve.
The orchestra is an analogy for mixing. POD learns its patterns from data; the patterns do not necessarily correspond to separate physical processes.
THE ACTUAL CLIMATE DATA
Meet the modes.
These are our project's real patterns. Explore one, combine several, or watch their observed strengths change through the historical record.
Mode 01 · Air temperature
One RMS coefficient amplitude
90° N90° S
−1 K
+1 K
Blue and orange show opposite signs of one pattern. Changing the sign of its coefficient reverses its contribution.
Observed monthly strength · Mode 011984 — 2024
Compression has a cost. All 41 supplied modes retain about 28.2% of the full weighted anomaly covariance spectrum. Better predictions cannot recover patterns outside this basis.
What's on the map?
All map views show anomaly contributions from the supplied POD representation. Daily playback combines the original coefficients with their spatial patterns and smoothly interpolates between days. No seasonal average or shift field is added. Wind uses purple–green for opposite directions; humidity uses brown–teal for negative and positive contributions. Temperature uses blue–orange. These are reduced anomalies, not absolute temperature, wind or humidity fields. The 1000 hPa slice can be below ground over high terrain.
02 / LEARN THE MOTION
Now give the patterns
a sense of time.
POD gives us a compact description. We still need a rule for how its strengths change. A neural ODE learns a rate of change, then a numerical solver follows that rule through time.
First, a pendulum we understand.
What makes a pendulum keep swinging, and why does it eventually stop? Gravity drives the swing; friction gradually takes energy away.
Here we supply examples of its angle, speed and how they change. A neural ODE learns the whole rule of motion. A physics-inspired model keeps the gravity we already know and learns the missing friction. The solver then turns each rule into a moving path. Because we know the true rule in this teaching example, we can check what each model gets right.
A PENDULUM IN STATE SPACEUntrained network
Teaching referencePhysicsNeural ODEHybridNeural ODE is highlighted
INSIDE THE LEARNED RULE
Watch the weights change.
Lines are actual weights; thickness shows strength. Nodes glow with their activation. Training updates these connections.
Positive weightNegative weight
2 inputs → 20 hidden units → 2 rates
Random starting weights
ANGLE PREDICTION ERROR · LOWER IS BETTER0 updates per network · same training states
Physics only—Gravity known; friction missing
Neural ODE—Learn the entire rate rule
Physics + learning—Keep gravity; learn the correction
Same starting angle, reference and first 12 model-time units. Both networks receive identical minibatches and update counts. This teaching system illustrates a useful physical prior; physics does not guarantee an advantage in every problem.
The solver builds the path.
A numerical method repeatedly follows those arrows. Small local errors can accumulate into a different trajectory.
Physics gives learning a role.
A universal differential equation can retain a physical rule and learn a missing correction. Try “Physics + learning” above.
What is actually training in this experiment?
A neural network is an adjustable rule made from layers of simple mathematical functions. Changing its weights changes its output. Here, a small tanh network trains in your browser on synthetic pendulum rates using gradient descent, which adjusts weights to reduce a measured error. The reference has restoring force and friction. The incomplete physics model retains the correct gravity rule and omits friction. The hybrid learns the missing acceleration while retaining the relation between angle and velocity. A fourth-order Runge–Kutta solver constructs the trajectories. This is a simplified rate-fitting demonstration; the research implementation also learns from integrated trajectory windows. Both networks see the same minibatches and update counts. The hybrid starts at the physical rule with zero learned correction. Its loss and trajectory errors are calculated from its actual predictions. Training here does not update the climate model.
From our notebooks · learning in shorter windows
Chaotic paths become difficult to match over long periods. Multiple shooting divides a long training trajectory into shorter pieces. Each piece can be fitted locally, while matching conditions or penalties link neighbouring pieces. This original Lorenz animation shows the training-window idea used in our benchmark work. Short-window agreement still needs a separate long free-running test.
03 / WEATHER IS A PATH. CLIMATE IS A PATTERN.
Different tomorrow.
A familiar butterfly.
Two almost identical starting states can lead to different weather. Climate asks a different question — what range of behaviour does the system visit, how often, and how does that change?
CSIRO · Why climate projections examine decades of weather ↗
Almost the same starting stateTeaching system
World AWorld B · tiny initial
difference
One tiny difference.
Two different futures.
The two worlds use exactly the same equations. Only the first starting coordinate changes. Watch the gap grow, or drag the time slider to inspect it.
WORLD A STARTS AT—
WORLD B STARTS AT—
The other two coordinates are identical.
DISTANCE BETWEEN WORLDS NOW0.001
1× the starting gap
See when the weather paths separate
Both still visit a similar range of states
The Lorenz system illustrates chaos; its coordinates are not atmospheric temperatures. Its distributions are finite samples, not proof of identical climates.
THE QUESTION CHANGES
→
“Will it follow this exact path?”
Short-term prediction checks trajectory error.
“Does it make a credible climate?”
Climate evaluation checks averages, variability, persistence and relationships.
04 / EXPLORE POSSIBLE FUTURES
Change the forcing.
Watch the response.
A scenario is a conditional “what if”. Choose a supplied forcing pathway, explore a saved project experiment, then try a teaching model in which the modes respond directly.
CSIRO & Bureau of Meteorology · How climate scenarios work ↗
SAVED PROJECT EXPERIMENT
An earlier project model responds to three possible forcing pathways. This view isolates its broad warming response; the changing weather patterns are not shown.
EXPLORE THE YEAR2050
Broad warming response · 2050
1000 hPa · change from 2025
−1 K
+1 K
Map colours use the same scale across pathways and years.
Supplied anthropogenic forcingW/m²
Saved forced response · change from 2025K
—
What the pathway supplies
An external push.
Forcing changes the energy balance. It is an input to a conditional experiment, not a prediction made by the neural network.
What we have to learn
The system's response.
How the modes respond, interact and remember past conditions must be identified and tested. A responsive map alone does not establish that.
What a credible result needs
More than a smooth curve.
Historical evaluation, physical consistency, stability and realistic variability all matter before using an emulator for decisions.
05 / WHAT WE DID THIS YEAR
Small models.
Big questions.
We investigated whether learning can improve a reduced atmospheric model, and where physical structure helps. The result is a set of experiments and a clearer picture of the trade-offs.
Start with systems
we understand.
Pendulums and chaotic Lorenz systems let us test learning, integration and training before facing atmospheric complexity.
Work in a shared
41-mode space.
The supplied POD representation connects daily atmospheric data to compact coefficient dynamics and reconstructed maps.
Learn the rule.
Learn a correction.
We explored structured regression, neural ODEs, hybrid UDEs, and extensions with memory and stochastic influences.
Evaluate the climate,
not just the fit.
Chronological evaluation examines prediction, free-running behaviour, variability, persistence and relationships between modes.
EL NIÑO MOTIVATES A FAMILIAR QUESTION
Can we predict
the next El Niño?
Could El Niño events become more frequent over the next 50 years? To explore questions like these, a model first needs to reproduce the climate’s natural rhythms. Here we test a first step: does our model sustain warm–cool swings over the tropical Pacific?
The ocean is the motivation.
The atmosphere is what we
model.
This curve measures a filtered air-temperature proxy at 1000 hPa over the Niño3.4 region. It is not sea-surface temperature, an official ENSO index, or a forecast of the next El Niño.
Bureau of Meteorology · El Niño and La Niña ↗
Reference swing size—
Our model · swing size—
Filtered regional air-temperature anomaly · KSaved free-running experiments
Supplied referenceOur model · one simulated
history
The same model can generate different possible histories. This one has a typical swing size among our saved runs. Averaging the histories would make individual swings less visible.
—
Supplied referenceSaved simulationOne deterministic trajectory
2014-10-02 to 2024-12-31 · Free run with no observed resets · Monthly means · Original coefficient units
—
How to interpret this comparison
These are existing saved experiments, not live climate training. The memory model has 32 saved stochastic members; the default shows member 1, while the optional ensemble mean averages them. An ensemble mean can be much smoother than an individual simulated history. The experiments differ in model structure and training configuration, so this is not a controlled attribution of improvement to any single component. Event-by-event alignment is not expected over an unreset decade. The current generation's chronological final quarter begins on 2 October 2014; the earlier poster's model generation used a different evaluation period.
Poster & sources
Sources & methods
Project evidence
The supplied dataset definition and inspected NetCDF files establish the 41-mode, four-field representation, daily coverage and retained variance. The latest report draft supplies the project framing. The poster provides the earlier hybrid architecture narrative. The saved neural runs and diagnostic tables provide the historical playback in the final experiment.
The website intentionally distinguishes the supplied representation, existing experimental outputs, live teaching models, and illustrative future responses.
Read the foundations
People & provenance
Daimon Byl · Kevin Horner · Benjamin Cottrell
Mechanical Engineering, University of Melbourne · 2026
With guidance from Professor Andrew Ooi and Dr Vassili Kitsios. Dr Kitsios prepared and supplied the POD dataset. Industry partner · CSIRO. Underlying atmospheric data · ERA5, ECMWF / Copernicus.