Pan’sLiFEYiming Pan’s GroupSHANGHAITECH UNIVERSITY中文
SCIENCE & INTELLIGENCE

AI4S × S4AI

Discover physics in data.
Explore intelligence in physics.

Two connected questions guide our work: how can data and learning help us understand complex physical systems? And how can physical structure help us understand and build learning systems?

AI → SCIENCE

AI for Science

Make complex dynamics readable.

SCIENCE → AI

Science for AI

Make learning mechanisms understandable.

01 / KOOPMAN–DMDPublic preprint

Turn evolving data into interpretable modes.

A movie of a wave often contains several rhythms at once. The Koopman operator perspective and dynamic mode decomposition (DMD) help separate modes from successive snapshots, revealing their frequencies, growth or decay, and spatial profiles.

Let the physical picture emerge.

Hover to preview. Click to keep. Explore until the picture is complete.

Connections between a driven lattice, physical structures and evolving data
Koopman–DMD

Extract frequencies, growth or decay, spatial profiles and weights to make dynamics readable.

Dynamics → Modes → Physical insight

Revealed 0 / 10
FIG. 01A Koopman–DMD research landscape · Conceptual illustrationLabelled figure ↗

What can a sequence of data reveal?

Select a quantity to see what each mode tells us.

SnapshotsKoopman–DMDModal information

How fast does it oscillate?

A signal can combine slow and fast oscillations. Modal frequencies separate these rhythms and help connect dynamics to band dispersion.

FIG. 02An illustration of modal concepts, not paper data. DMD approximates dynamical structure from snapshots; it is not the same as training a neural network.
02 / PINED-NETOngoing research

Build a physical network with light and electrons.

Could neural-network computation take place in real wave propagation? PINED-Net explores photon-induced near-field electron interactions: light shapes an electron wave, information passes through successive physical layers, and the output is read out.

PINED-Net conceptual architecture with electron waves passing through light-driven physical layers and readout
FIG. 03Simplified PINED-Net concept. Layer count, wave propagation and the output spot are illustrative.
  1. 01

    Input information

    Bring information into an electron wave.

  2. 02

    Light-driven physical layers

    Light–electron interactions shape the wave state across layers.

  3. 03

    Propagation & readout

    Turn the output of successive physical processes into readable information.

This is ongoing research. We present the basic idea here; implementation details and results will be described in future work.

Explore the physics of PINEM ↗
03 / TOPOLOGY & LOCALIZATIONPublished

Why do waves spread—or stay localized?

Topology asks how global structure shapes wave behavior. Localization asks how waves remain confined. We aim to connect these physical questions with dynamical features in data.

Conceptual phenomenological correspondence between extended Fermi-liquid states and many-body localization
FIG. 04Redrawn from Pan, He and Pan, J. Phys.: Condens. Matter 38, 075702 (2026), Fig. 4 (original CC BY 4.0). A conceptual illustration of a phenomenological correspondence.

Physical foundation · Many-body localization and Fermi liquids

In work co-first-authored by Jinze He, we propose a phenomenological correspondence between extended Fermi-liquid quasiparticles and local integrals of motion in many-body localization, and discuss normal-state instabilities. This offers physical clues for comparing many-body states and their observable features.

Read the localization paper ↗
Explore the numerical example in the paper

Figure 7 illustrates a 12-spin XXZ system and the competition among kinetic energy, disorder and interactions. This finite-size example is not a rigorous phase-boundary determination in the thermodynamic limit.

JPCM 38, 075702 (2026), Fig. 7
04 / SCIENCE FOR AI

What does a neural operator actually learn?

Predicting the next frame is a starting point. We also ask how a network uses physical information, whether its learned structure can be explained, and whether physical operators and wave propagation can become trainable information processors.

Public preprint

MH-RG DeepONet · Bringing physical information into learning

A neural operator learns a mapping between functions. Here, the initial field and coordinates enter branch and trunk networks. Physical descriptors inform both representations before they are combined to predict field evolution. The multi-head structure offers a way to investigate model behavior.

Read the MH-RG DeepONet paper ↗
Initial field, coordinates and physical descriptors feed the MH-RG DeepONet branch and trunk networks to predict a field
FIG. 05Redrawn from the public MH-RG DeepONet architecture. Waveforms are illustrative and do not represent errors or performance.
Explore the model-analysis figures

Multi-head mechanism analysis and noise tests from the public paper (Figs. 3 and 4). Reliability should be assessed together with test conditions and measured errors.

MH-RG DeepONet, Figures 3 and 4

Questions we are pursuing

How does physics help learning?

Physical descriptors can bring relevant structure into a model. We ask when they improve prediction or generalization, and which information actually matters.

How can we understand neural operators?

Can modes, symmetries and multiple scales explain how a model organizes information? Interpretability needs controlled comparisons and testable mechanisms, beyond visualization alone.

Can physical operators be intelligent?

If intelligence means trainable, adaptive information processing, what computations can waves and physical interactions perform? PINED-Net explores this possibility; the broader question remains open.

05 / SELECTED WORK

Follow the papers further.

All group publications ↗

Illustrations are conceptual, with some redrawn using AI assistance. Consult the original papers for numerical results and conditions of validity.