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Gas adsorption simulation: uptake, grand canonical Monte Carlo, classical density functional theory, and density-field learning.

A physics-first account of molecular representation, electronic structure, forces, statistical mechanics, and dynamics for molecular machine learning.

How periodic representations support crystal prediction and generation—and why relaxation, first-principles validation, and synthesis remain decisive.

Why deeper graph networks face under-reaching, over-smoothing, and over-squashing—and how topology determines which remedy helps.

A unified derivation of diffusion and flow matching through conditional probability paths, marginalization identities, and simulation-free regression.

How continuous-time Markov chains transport categorical probability, how their rates become learnable, and how generator matching extends across modalities.

Statistical mechanics: from Newton's equations to ensembles, thermostats, barostats, Monte Carlo, and connections to generative modeling.

How invariant attention scores, equivariant values, and energy-based force prediction turn geometric Transformers into practical interatomic potentials.

How canonicalization, local frames, frame averaging, and probabilistic symmetrization create geometric models—and why continuity is difficult.

How path measures connect Jarzynski's equality, free-energy estimation, annealed importance sampling, diffusion models, and GFlowNets.

Molecular graph generation and reaction modeling viewed as constrained structured prediction, from representation and symmetry to synthesis-aware evaluation.

GFlowNets from a probabilistic-ML perspective: reward-proportional sampling, training objectives, and connections to MaxEnt RL and variational inference.

Protein design as sequence–structure–function inference, from inverse folding and backbone diffusion to computational filters and experimental evidence.

From genomic sequence models and noisy single-cell measurements to perturbation prediction and the stronger requirements of a virtual cell.

Flow matching beyond Euclidean space, from tangent velocity fields and geodesic conditional paths to product manifolds for molecular geometry.

Why permutation symmetry leads to message passing, how familiar GNNs instantiate it, and why graph Transformers still need structure.

Heterogeneous electrocatalysis: the energy storage problem, why oxides matter, the solid-liquid interface, and why real catalyst design is hard.

Why drug discovery is a sequence of linked inference problems—from target validation and molecular binding to exposure, safety, and clinical benefit.

How HACO, a Human–AI Co-discovery system, produced MaskGXT, a competitive generative model for crystal structure prediction.

MADField predicts the full 3D adsorbate density field in nanoporous materials, turning slow gas-adsorption simulation into a single forward pass.

Where machine learning enters electronic-structure theory, from neural wavefunctions and learned functionals to Hamiltonians and energy surfaces.

A material is more than a formula: discovery must connect periodic structure, competing phases, target properties, processing, and experimental formation.

How molecular representations, conformers, data splits, pretraining, and uncertainty determine what a property-prediction benchmark actually measures.

A practical bridge from molecular dynamics to enhanced sampling, metadynamics, collective variables, and recent ML approaches for rare molecular events.

How learned energy surfaces become molecular dynamics, why rollout stability differs from static accuracy, and how to validate observables.

How ODEs and SDEs transport probability, why scores appear in reverse-time diffusion, and how probability-flow ODEs match SDE marginals.

An introduction to protein structure, function, and computational design — from amino acids to the RFDiffusion/ProteinMPNN pipeline.

How metastable protein conformations become equilibrium ensembles and kinetic models, and what learned samplers must preserve beyond structural plausibility.

How sequence, alignments, residue graphs, backbone frames, surfaces, and multimodal objectives shape what protein embeddings can support.

How coevolutionary constraints, pairwise geometric reasoning, residue frames, and all-atom diffusion shaped AlphaFold—and where structure prediction stops.

Quantum chemistry and density functional theory: from the Schrödinger equation to Kohn-Sham DFT and modern deep learning approaches.

How geometric graph networks move from invariant distances and angles to equivariant coordinates and vector channels—and what directionality buys.

Understanding the spherical equivariant layers that power modern molecular neural networks, from group theory foundations to Clebsch-Gordan tensor products.

How irreducible rotation types, spherical harmonics, and Clebsch–Gordan tensor products create expressive equivariant neural-network layers.

A concrete account of group actions, invariance, equivariance, and feature types for geometric machine learning.

Three routes to the Fokker-Planck equation—physical intuition, heuristic discretization, and a rigorous derivation with Itô calculus.

How generative models respect molecular geometry, how guidance turns sampling into design, and why oracle scores must survive experiment.

Two derivations of graph convolution—from Laplacian spectral filters and permutation-equivariant linear maps—and what each reveals and hides.

Graph neural network expressivity through multiset aggregation, the Weisfeiler--Leman test, its blind spots, and the cost of stronger models.