Space
What distinctions should the representation preserve?
Organise scientific states, coordinates and scales so that relevant structure, symmetries and uncertainty can be represented.
Xu Lab · Scientific Learning & Discovery Systems
Learning, evidence, and discovery belong together.
We seek to understand and improve how scientific discovery happens. Our long-term mission is to develop principles and methods of scientific learning and discovery grounded in mathematics, information, and computation. We ask how scientific systems can choose meaningful variables and scales, distinguish competing explanations, acquire informative evidence, and revise models, concepts, and questions as new evidence emerges.
Our research connects the design of scientific learning systems, the creation and acquisition of evidence, and mathematical and data-science exploration.
01 · Connected design choices
Space, interaction and learning shape one another.
We study these as connected choices within a scientific learner: what it can represent, which relationships it can express and how it changes with evidence. Together, they form part of learning-system design, alongside our work on evidence engineering and mathematical exploration.
Interaction
Which relationships should the system expose?
Design how information is exchanged, transformed and combined, from local relationships to collective and cross-scale effects.
Learning
What update process turns evidence into reusable knowledge?
Design learning goals, feedback and constraints together to study how the system changes as evidence arrives.
The interlinked forms are a visual metaphor for this mutual shaping: representations make some relations expressible, interactions shape what can be learned, and learning can reveal the need to change both.
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A conceptual illustration of how representations, interactions, and learning shape one another. Interlinked bands show spatial arrangements, relationships, and revision; the forms are a visual metaphor.
Evidence makes revision possible.
Choose observations, perturbations and experiments that can distinguish competing explanations and change the next learning step.
Tests of proposed mechanisms and designs return new evidence, revised questions and constraints to the learner.
Explore evidence engineeringResearch horizon
Methods within our mission
Space and representation design are central methods within this mission. We study them alongside model and system architectures, learning objectives, evidence acquisition, research infrastructure, and scientific evaluation. Our aim is to develop methods whose value can be tested through scientific understanding, reliable design, and further research.
What can be carried from one scientific setting to another, and what must remain specific to the question and its evidence?
Explore the research horizon02 · Research principles
Make scientific ideas open to challenge.
These principles guide how we represent a scientific problem, choose evidence and test an explanation or design. They connect the three research Pillars through a shared approach to inquiry.
Mechanism-aligned
Representations and objectives should preserve distinctions that matter to the scientific mechanism.
Evidence-efficient
The next dataset or experiment should reduce uncertainty that matters to a decision.
Uncertainty-aware
A scientific system should expose what it does not know and where its conclusions may fail.
Compositional
Reusable primitives, interactions, and operators should support analysis across systems and scales.
Testable
Explanations should imply controls, perturbations, or observations that could challenge them.
Design-oriented
Learned structure should return to experiment through candidate, molecule, material, or system design.
03 · Research directions
Current work, next connections, long-term questions.
These are planning windows. Expansion will follow research progress and validation.
Now
Mechanistic questions in molecular and materials science
We develop and test AI methods for mechanism understanding, discovery, and design through scientific questions and feedback from experiments and simulation.
Over approximately five years
Building reusable scientific capabilities
We aim to develop reusable representation and model methods, scientific system architectures, research infrastructure, evidence-acquisition strategies, and evaluation systems that support mechanism understanding and reliable design.
Over approximately five to ten years
Testing principles across systems
We aim to extract mathematical, computational, and system-design principles and test how these methods and capabilities transfer and combine across broader scientific fields.
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