Ideas we're actively researching
This page is our open sketchbook: small, interactive models of the problems we are working on right now, from liquefaction hazard and critical-mineral slope stability to physics-informed reconstruction of legacy data. Nothing here is a pre-rendered picture; each one solves the real engineering and physics live in your browser.
They are meant to be played with. Pull the sliders, flip the toggles, and get a feel for the topics, and for the questions we are most active on at the moment. Our capabilities come first, then our research focus areas.
Physics-Informed Modeling
Engineering models that answer to physics. A rainfall-triggered slope is solved live with the infiltration and infinite-slope equations, not a fitted curve.
Rainfall-triggered slope failure
Iverson's rainfall-infiltration equation, solved here for the pore-pressure head and then the infinite-slope factor of safety. This is the physics a PINN learns in Cao & Gong (2025). Defaults are the Minor Creek Landslide (Iverson 1984). Press play, or move the controls.
How this works
Infiltration follows Iverson's (2000) linearization of the Richards equation,
∂ψ/∂t = D₀cos²α · ∂²ψ/∂Z², with the closed-form response to a
rainfall flux of normalized intensity I/K over duration T. Pressure head is bounded by Iverson's β line, the maximum sustainable with the
water table at the ground surface, and sustained I/K is capped at 1 (rainfall above the saturated conductivity runs off rather than infiltrating). The infinite-slope factor of safety is
FS = tanφ/tanα + (c' − ψγwtanφ)/(γsZ sinα cosα).
Failure is FS < 1. Defaults reproduce the Minor Creek Landslide (Iverson 1984; D₀=10⁻⁶ m²/s, γs=22, γw=9.8 kN/m³,
slip at 6 m, water table 2 m). This is the model a PINN learns in Cao & Gong (2025); curves are computed live here.
Agentic Intelligence
Agentic decision workflows. A rare-earth deposit is taken from grade, recovery, and basket price through a cutoff and whole-pit economics to a mineability call.
Critical-mineral mineability decision
A decision agent reads the deposit's block model and the market context, sets the economic cutoff grade, classifies every block as ore or waste, and returns the project decision. Grades follow a carbonatite-style rare-earth body (illustrative grades, not a specific deposit). Move the context sliders.
How this works
The agent sets the milling cutoff grade g* = processing cost / (10 · recovery · basket price)
(TREO in %), then mines the whole pit and processes only blocks above g*. Per-tonne ore margin is
10·g·recovery·price − processing − mining·(1+strip), and project value is a discounted cash flow,
NPV = margin · throughput · annuity(8%, life) − capex. Fixed assumptions: mining $5/t, 2 Mt/yr throughput,
8% discount, mine life capped at 30 yr. Payability, separation and refining, royalties and tax are not modeled, so the NPV is an optimistic screening figure
rather than a feasibility estimate, and the “agent” is a deterministic cutoff-grade rule (the $25/kg default basket is broadly consistent with mid-2026 NdPr-driven prices).
Grades emulate a carbonatite rare-earth deposit; all figures computed live.
AI Infrastructure
The compute behind the models: a four-node RTX 5060 Ti cluster sized for parallel, physics-informed machine-learning workloads.
The compute fleet
A four-node GPU cluster turns field data into trained physics-informed models. Pick a workload and scale the jobs to see how the fleet parallelizes it, and where the 2.5 GbE link sets the honest limit.
How this works
Each node is an NVIDIA RTX 5060 Ti 16GB (Blackwell GB206: 4,608 CUDA cores, 448 GB/s, 23.7 TFLOPS FP32 at the 2.57 GHz boost, 180W);
four nodes give 64GB, 18,432 cores and 94.8 TFLOPS, with four 4TB Samsung 990 PRO NVMe (7.45 GB/s sequential read each) and a 2.5 GbE link.
Independent jobs (ensembles, parameter sweeps, batch inference) parallelize across the four nodes, so wall-clock
speedup = jobs / ceil(jobs/4), up to 4×. Tightly-coupled distributed training must synchronize gradients every
step; over a 2.5 GbE link (~0.3 GB/s) that communication dominates, so it is bandwidth-bound and best run on a single node.
Geo Hazards
Regional liquefaction hazard mapping with physics-informed machine learning: triggering, probability, epistemic uncertainty, and consequences on one shared earthquake.
Liquefaction hazard, physics-informed · Duwamish corridor
Two views of the same ground. Choose a scenario earthquake, then read it as a SoDo soil column (the triggering mechanism, depth by depth) or as a probability map across the corridor (where it manifests). Both views share one physics: cyclic demand against cyclic resistance (Boulanger-Idriss), and an explicit probability of liquefaction. Scenario shaking is set to representative Puget Sound events, including the 2001 Nisqually earthquake.
How this works
Triggering (column). Cyclic stress ratio CSR = 0.65·(aₘ₃ₓ/g)·(σ₃/σ₃')·rₗ is weighed against
cyclic resistance CRR₃.₅ from the clean-sand (N₁)₆₀cs (Boulanger & Idriss 2014), scaled by the magnitude scaling
factor MSF and the overburden factor Kσ; FS = CRR·MSF·Kσ/CSR, with liquefaction at FS < 1. Probability (map). The same factor of safety is mapped to an
explicit probability of liquefaction Pₜ = 1/(1+(FS/0.8)3.5) (Juang, Jiang & Andrus 2002, SPT mapping) for each geologic cell of the corridor, evaluated at a representative 4.5 m depth. These coefficients were fit to the NCEER (Youd et al. 2001) factor of safety; the authors found the mapping insensitive to the MSF and rₗ choice, so it is applied here to the Boulanger-Idriss FS as a close approximation.
Uncertainty (epistemic vs aleatory). The probability itself is uncertain. Limited soundings leave the layer's
representative (N₁)₆₀ uncertain (Phoon & Kulhawy 1999 give SPT COV of roughly 0.2–0.6); propagating that through the
triggering model (first-order second-moment) gives a reducible band on Pₜ that narrows as 1/√n with more borings, toward an
irreducible floor from model and natural variability. Consequences. Reconsolidation settlement integrates the post-liquefaction
volumetric strain εᵛ = 1.5·exp(−2.5·Dᵣ)·min(0.08, γᵐᵀᵅ) (Ishihara-Yoshimine 1992; Idriss-Boulanger 2008) over the
profile; it saturates once the column fully liquefies. Lateral spread uses the Youd-Hansen-Bartlett (2002) ground-slope model (driven by the ground slope toward the channel, not the free-face ratio), whose strong
magnitude term means a near-field M7 and a distant M9 can differ sharply at one site. The Youd-Hansen-Bartlett data are drawn largely from
magnitude 6 to 8 events; data above M8 are sparse, so the Cascadia M9 spread is the least-constrained value here (Youd et al. 2002 still predict the few
M9.2 1964 Alaska displacements within a factor of two, but note more data are needed at large magnitude).
Scenarios. Accelerations are representative site (ground-surface, soft-soil) peak values that drive triggering, not regional rock motion: the 2001 Nisqually rock motion was about 0.06 g, amplified to roughly 0.2 g at the SoDo / Harbor Island artificial fill that liquefied; a shallow Seattle Fault M7 is near-field and high-amplitude (~0.45 g) but short; a Cascadia M9 is more distant yet basin-amplified (~0.30 g) and very long. Durations are approximate significant durations by event type; the simulated Cascadia M9 in Seattle is near 100 s, about four times Nisqually (M9 Project). Geology. The corridor is a schematic of the Duwamish fill axis; the marked points are its loosest-fill cells, illustrative of where 2001 liquefaction concentrated along the buried river meander, not surveyed locations. Probabilities are computed live.
Critical Minerals
Rare-earth mining as two slope-stability problems: a coal-ash impoundment to keep stable and a carbonatite open pit to steepen as far as safety allows.
The geotechnics of getting it out
Rare-earth mining is two slope-stability problems. A coal-ash impoundment is a dam you must keep stable; a carbonatite open pit (Mountain Pass scale, ~180 m) is a rock wall you want as steep as safety allows. Both are live limit-equilibrium models, move the controls and watch the factor of safety respond.
How this works
Ash dam. The downstream slope's factor of safety follows the phreatic surface (hw = ash elevation + pool depth):
FoS = c'/(γz·sinβcosβ) + (1 − m·γw/γ)·tanφ'/tanβ, m = hw/H (Duncan, Wright & Brandon 2014, Eq. 7.12 with slope-parallel seepage). Open pit. A Culmann
planar-wedge limit equilibrium minimised over the failure-plane angle: FoS = [c'L + W·cosθ(1−rₜ)tanφ'] / (W·sinθ),
with W the wedge weight and L its length (Wyllie 2018, Eq. 1.6; c' and φ' are rock-mass strengths, not joint strengths); steepening the wall lowers FoS but also the strip ratio (waste:ore = (H/tanψ)/Wore).
Defaults are Mountain Pass scale (180 m, γ=26 kN/m³). The ash grade, 481 ppm total REE, is the median for U.S. coal fly ash, where Taggart et al. (2016) define total REE as the lanthanides plus yttrium and scandium (elemental, not oxide). Both are simplified limit-equilibrium models, computed live.
Legacy Data
Turning scattered legacy well records into a continuous, physically valid groundwater field by solving the flow equation rather than blindly interpolating.
From scattered wells to a physically valid field
Decades of legacy groundwater records are a handful of scattered well readings. Turning them into a continuous head map by blind interpolation puts a bull's-eye around every well, a field that quietly violates the flow equation: it implies water appearing and vanishing across the site. The physics-informed reconstruction instead solves Darcy flow (Laplace, ∇²h = 0) honouring the same wells, so the map honours mass balance between the wells and its flow lines are physically consistent.
How this works
Steady groundwater flow obeys Darcy's law with mass conservation, which for constant transmissivity reduces to
Laplace's equation ∇²h = 0; a real head field therefore has no interior peaks or pits (maximum
principle) and conserves water. Naive is inverse-distance weighting: it honours the wells but is not harmonic, so
every well becomes a local extremum (bull's-eye) and the discrete ∇²h residual is large, implying
spurious recharge and discharge. Physics-informed solves Laplace on the grid honouring the same well heads with a
regional gradient as boundary condition (here assumed known; in practice it would be estimated from the wells, and is the same data-plus-PDE objective a PINN minimises), so the residual collapses toward zero between the wells
and the flow field is physical away from them; the residual concentrates at the pinned wells, where point data meet the homogeneous-aquifer assumption. The true field is a synthetic harmonic head used to place the wells (its tiny residual reflects harmonicity in physical, not index, coordinates); reduce the well count
to see naive degrade into disconnected bull's-eyes while the physics-informed map stays coherent. Computed live.