Research

The equations are stiff, coupled, and on moving boundaries. Standard neural solvers stall on them by orders of magnitude.

What this area is

We build numerical methods that solve the governing equations of electrochemistry and transport,
and that can also be run backwards. The distinguishing feature is differentiability: gradients pass
through a converged solution, so a single code predicts forwards, fits parameters to measurements,
and optimizes a design, instead of three separate codes that must be kept consistent by hand.

Why we work on it

The equations are not in doubt. Poisson–Nernst–Planck transport, Butler–Volmer kinetics, the point
defect model for oxide growth: these have been written down for decades. The difficulty is solving
them where measurements are made, since the residual scales differ by many orders of magnitude, the
systems are tightly coupled, and the domain boundary moves as the material grows or dissolves.

Physics-informed neural networks were supposed to make these problems tractable and to make
inversion natural. In practice they stall around a percent-level residual on exactly the equations
electrochemistry needs, which is far too coarse to say anything about a mechanism. We wanted to know
why, and then to fix it.

What we do here

Neural spectral-element methods. We traced the accuracy floor to three structural causes acting
together: randomly sampled collocation points, serial automatic differentiation, and a stochastic
loss landscape. Replacing random sampling with fixed spectral nodes and automatic differentiation
with a precomputed differentiation matrix makes the loss deterministic, and residuals fall to
10⁻⁹–10⁻¹⁰ on stiff transport benchmarks, roughly seven orders below where standard formulations
stop improving.

Diagnosing and stabilizing physics-informed solvers. Physics-based non-dimensionalisation
extends stable simulation of passive-film growth from about an hour to 250 hours of exposure, and
adaptive weighting compresses a four-to-six order imbalance between loss terms to order one, giving
film thickness within 2.2% at every applied potential while tolerating 5% measurement noise.

Benchmarking what actually earns its cost. We compared eleven stabilisation strategies against a
thousand-cell finite-volume reference on the same problem, and found a configuration that matches
the best accuracy while saving 3.2 hours of training per run, which matters when an inverse-design
loop calls the solver thousands of times.

Numerical schemes for fractional moving boundaries. The standard front-fixing transformation is
unavailable for time-fractional operators, because there is no chain rule for fractional
derivatives, and a substantial applied literature has used it anyway. We derive a fixed-grid scheme
that carries a per-node crossing time instead, together with exact solutions the field had lacked as
benchmarks.

Second-order training at scale. Natural-gradient methods are far more accurate than standard
optimizers and far too slow at scale. Randomized sketching compresses the operation and brings
networks with millions of parameters within reach.

And we publish when the neural method is the wrong tool. In one case a plain finite-difference
scheme reproduced a published moving-boundary result four orders of magnitude faster than the
neural solver it was compared with, and the advantage that had been attributed to the network turned
out to be a property of the comparison. We think this is as much a contribution as a new method.

Systems and applications

Lithium symmetric cells and solid electrolytes · passive films on stainless steel in reactor water ·
porous battery electrodes · alkaline oxygen evolution · solid oxide electrolysis and fuel cells ·
any transport problem where the parameters must be recovered from sparse measurements

From an image of a real electrode to a predicted spectrum, with no equivalent circuit anywhere.

What this area is

We model what happens at and inside an electrode: the charged layer at the surface, the reaction
that crosses it, and the pore network the ions travel through to reach it. The commitment is to
compute these from transport and kinetics rather than to represent them with fitted circuit
elements, so that the numbers we report mean something outside the conditions they were measured in.

Why we work on it

An impedance spectrum takes minutes to record and contains, in principle, a great deal about how an
electrode works. The field reads it by drawing an equivalent circuit, a handful of resistors and
capacitors chosen because they reproduce the curve. The circuit fits, tells you nothing about why
the electrode behaves that way, and stops working when conditions change.

The cost of that convention is visible in problems the field has not resolved. Electrode tortuosity
measured by impedance and by tomography have disagreed by roughly a factor of two for about twenty
years. Degradation is predicted with power laws whose exponents are fitted rather than derived.
Charge-transfer rates are still empirical parameters even in models where everything else is
computed.

What we do here

Impedance from a resolved microstructure. We take the segmented three-dimensional image of a real
electrode and solve the pore phase directly as a complex-valued finite-volume network with a
frequency-dependent interface condition, with no transmission-line model anywhere. The method
reproduces the analytic limit to 2% and an independent implementation to 0.22%.

The carbon-binder domain and the tortuosity discrepancy. Including a sub-voxel binder film raises
the apparent tortuosity of real graphite from 1.92 to 3.31, which carries it out of the tomography
band and into the impedance band, and closes the twenty-year gap from the modelling side.

Impedance from the reaction mechanism. Solving size-modified transport together with
Frumkin–Butler–Volmer kinetics gives polarisation and Nyquist responses that follow from the
chemistry rather than from a fitted circuit topology.

Passive-film growth and corrosion. Inverting the point defect model against measured film
thickness recovers a mechanism rather than an empirical growth law, and gives a ten-year prediction
that differs from the fitted power law by a factor of several, with the difference attributable.

The last fitted parameter. Nearly every rung in our multiscale chain is now computed: atomic
structure, interatomic forces, interfacial structure, ion transport, device response. The
charge-transfer rate is not; it is still Butler–Volmer with an empirical coefficient. Computing it
from electron-transfer theory, including the prediction of lithium-plating onset, is the work that
closes the chain.

Manufacturing. With industrial partners we are building physics-informed surrogates for dry
electrode manufacturing, where powder spreading, binder infiltration and laser sintering set a
microstructure that cannot be observed while it forms.

Systems and applications

Lithium-ion and solid-state batteries · graphite anodes under fast charging · dry and laser-sintered
electrodes · solid electrolytes and their interfaces · stainless steel in boiling-water reactor
chemistry · alkaline oxygen evolution and water electrolysis · solid oxide cells

Industrial partners in the electric-vehicle battery supply chain fund parts of this work.

One free energy, differentiated automatically, from gas separation to battery interfaces to freezing.

What this area is

Classical density functional theory predicts how a fluid arranges itself near a surface, starting
from a free-energy functional rather than from a fitted curve. We have rebuilt it as differentiable,
GPU-native code, so that every derivative the theory requires is obtained automatically and exactly,
and so the theory can be run in time, fitted to data, and inverted toward a design.

Why we work on it

Push a fluid against a surface and it stops behaving like a bulk fluid. Its density oscillates in
layers a few molecules deep, ions of one sign crowd in while the other is pushed away, and the
packing at the wall bears little resemblance to the packing a nanometre out. Almost everything that
matters at an interface is decided inside that layer.

The standard tools average it away. Adsorption gets a fitted isotherm measured on one material.
The electric double layer gets a theory that treats ions as points with no size at all. Both hold up
until the interface becomes crowded, which is exactly the situation in a nanopore, in a concentrated
electrolyte, and at high voltage. There the classical description is not slightly inaccurate; it can
be wrong by orders of magnitude and wrong in the direction that matters.

Classical density functional theory has been able to do better since the 1980s. What kept it from
routine use was practical: every new free-energy model needed its derivatives worked out by hand,
and every code was written for one host material and one fluid.

What we do here

Adsorption and separation without a fitted isotherm. For carbon dioxide in a porous aluminium
framework, the calculation reproduces the room-temperature uptake curve to 0.44 mmol g⁻¹ with
nothing fitted, and settles what the material is doing. The selectivity from equilibrium
thermodynamics is about 4 while the measured selectivity is between 350 and 600, so the material
separates kinetically, by admitting one gas faster, not by binding it more strongly.

Ion transport at electrified interfaces. Coupling transport to interfacial structure lets us
follow how an electrode charges rather than assuming a capacitance. Where the screening length and
the ion diameter are comparable, treating ions as objects with size gives a bounded, asymmetric
capacitance, while point-ion theory diverges by up to nine orders of magnitude.

Learning the functional rather than replacing it. The approximations inside the free energy set
the ceiling on everything else, so we make its coefficients learnable and tune them through the
solver. The model recovers the exact known result for simple fluids without being told about it, and
predicts the density at a wall to within one to two percent of direct simulation, with the
bulk-versus-interface tradeoff quantified rather than hidden.

Freezing and nucleation. The same free energy describes a liquid ordering into a solid. We
compute crystal–fluid interfacial tensions and follow how a nucleus forms, and we document where the
method currently falls short, since a benchmark that reports only successes is not a benchmark.

Inverse design. Because sensitivities pass through a converged solution, the theory runs
backwards: from a target separation to the material that would deliver it.

Systems and applications

Metal-organic and covalent organic frameworks, zeolites, aluminium formate · carbon capture and gas
separation · hydrogen storage · solid electrolytes and battery interfaces · molten salts and ionic
liquids · concentrated electrolytes and supercapacitors · crystallization and polymorph selection

Getting the atoms right, because everything downstream inherits the error.

What this area is

This area answers one question from two directions: what are the atoms doing. The first direction is
forces, where we build machine-learned interatomic potentials that reach quantum accuracy at the
scale where transport properties live. The second is arrangement, where we determine and design
atomic structures by gradient rather than by stochastic search. The two feed each other, since a
potential is only as good as the structures it was trained on, and a structure is only as
trustworthy as the forces used to relax it.

Why we work on it

Inside a molten salt reactor, a fluoride melt at 700 °C circulates against a steel wall it is slowly
dissolving. You cannot put an instrument into it. Quantum mechanical simulation would describe the
chemistry correctly but reaches a few hundred atoms for a few picoseconds. Classical force fields
reach the right scales by assuming a chemistry molten salts do not obey.

Learned potentials close that gap, but they rest on an assumption: that an atom's energy is set by
its immediate neighbourhood. That assumption is what makes them work, and it is also where they
fail. Two uranium ions can sit in fluoride cages that look identical and carry different oxidation
states, because the difference is written in the electron count of the system rather than in either
neighbourhood.

Structure has a parallel problem. A crystalline material has sharp diffraction peaks and a solvable
structure. A glass or an amorphous anode has a few broad humps, and many arrangements of atoms
reproduce them equally well.

What we do here

Charge decided globally, so oxidation state becomes visible. A neural network reads each atom's
environment and outputs an electronegativity and a hardness; one global calculation, constrained so
total charge is conserved, converts these into the charges of every atom at once, and those charges
drive the electrostatics explicitly. The whole chain is differentiable, so the forces include charge
flowing between atoms as they move.

What a molten-salt potential must include. We train several architectures on identical quantum
reference data and compare them on the properties that matter downstream, asking whether long-range
electrostatics and dispersion must be treated explicitly or can be absorbed. This is usually
asserted; we measure it.

Transport coefficients computed rather than fitted. Equilibrium and non-equilibrium molecular
dynamics give viscosity, thermal conductivity and diffusivity directly, across the full operating
range of a system.

Anomalous transport in amorphous electrolytes. Fifty-four trajectories across three compositions
falsify the trap-limited explanation of subdiffusive lithium motion on two independent observables,
and show that extrapolating from above the crossover overestimates room-temperature diffusivity by a
factor of 1.4 to 1.7.

Structure by gradient rather than by chance. Treating atomic positions as parameters and pushing
gradients back from a computed diffraction pattern, with chemical coordination enforced as a
constraint, fits silica, germania and lithium thiophosphate electrolytes above R² = 0.955 within
5,000 steps from a single dataset each.

Inverse design of alloy structure. Generating high-entropy alloy configurations by inverse design
is about a thousand times faster than the standard quasi-random construction and makes cells beyond
40,000 atoms practical; two independent groups have built on it. Extending the same idea to
short-range order reaches a target arrangement 6 times faster and 8 times more accurately than
stochastic search, and then reaches a target stiffness.

Representations that let datasets be pooled. Extracting the local chemical environment of an
adsorption site as a graph allows datasets collected with different geometries to be merged into one
model.

Systems and applications

Molten fluoride salts and uranium species for advanced reactors · refractory and high-entropy alloys
under irradiation · graphite anodes and grain-boundary transport · lithium thiophosphate and other
amorphous solid electrolytes · silica and germania glasses · catalytic metal surfaces

What a measurement can determine, in corrosion, degradation and anomalous transport.

What this area is

Given a measurement and a model, we ask a question that is usually skipped: could the data have
supported a different answer just as well? We build the diagnostic into the inversion rather than
running it afterwards, we anchor each inversion on a case whose answer is known independently, and
when the data do not determine the parameter we say so instead of reporting a number.

This is the thread that runs through everything else on this site. Differentiability supplies the
capability; identifiability is the brake.

Why we work on it

A recovered parameter is a claim about a system. Most of the time the claim is made without a
statement of whether the measurement could have distinguished it from an alternative, and when that
is checked the results are uncomfortable.

Fitting the same solid-electrolyte-interphase dataset under two equally defensible conventions gives
non-overlapping confidence intervals on six of nine series. Residuals in coulometric titration are
so strongly autocorrelated that 221 data points carry the information of about six, and standard
intervals are too narrow by factors between 1.2 and 7.1. Attribution of battery degradation from
capacity fade reaches 37.5% against a 29.2% majority baseline, and adding a differential-voltage
fingerprint makes it worse. Electrode microstructures with bit-identical porosity, tortuosity and
specific surface area differ in impedance by 59.2%, so a spectrum does not determine a structure.

None of these are failures of the measurements. They are limits on what the measurements can decide,
and reporting them is more useful than reporting a number that the data do not support.

What we do here

Identifiability inside the inversion. Profile likelihood and bootstrap run as part of recovering
a corrosion mechanism, not as a post-hoc check. Of five parameters in the point defect model, one is
undetermined by three exposure times and a second is weakly determined, and 95% of the fit statistic
rests on three data points.

Instruments, not just estimates. For fractional-order transport we ship three things alongside
the recovered parameters: an adequacy test that confronts three structurally independent estimates
of the same order and rejects the model when they disagree; an identifiability certificate that
returns, constructively, the most different answer the measurement cannot rule out; and a planner
that converts either verdict into the experiment that would settle it. On published data the method
rejects the transport reading rather than reporting a number, which is the outcome it was built to
make visible.

How much data an answer actually needs. For general memory kernels, only an effective order is
robustly recoverable from a single curve; the fine-grained spectrum is not identifiable at all.
Twenty cells from two public datasets span 1.2 to 2.2 decades where 3.1 are required.

Robust inference for growth laws. Moving-block bootstrap on strongly autocorrelated residuals,
and a demonstration that several memoryless models with exactly square-root asymptotics present
apparent exponents anywhere from 0.10 to 1.00. An exponent alone is not evidence of anomalous
transport.

Silent failure modes. A physics-informed inversion can satisfy the data while violating the
equation it was supposed to enforce. This is caught only by re-solving forward, and we document it
so others can check for it.

Validation against fixed answers. Wherever possible we anchor on a case where the true value is
known analytically. Applied to a closed-form porous-electrode problem whose exponent is exactly
one half, our estimator returns 0.500.

Systems and applications

Passive films and corrosion in reactor water · solid-electrolyte interphase growth in lithium metal
cells · lithium diffusion in amorphous sulfide electrolytes · porous battery electrodes and impedance
· public battery ageing datasets · experimental design for any campaign where the measurement is
expensive and the question is whether it will settle anything