Forest Informed Neural Networks (FINN)

• FINN is a hybrid dynamic forest modeling framework where deep neural networks replace selected demographic process equations while retaining mechanistic state transitions.
• The method employs joint calibration of neural and mechanistic parameters to correct structural misspecification and improve accurate predictions of forest dynamics.
• Empirical results on Barro Colorado Island data show that the hybrid approach enhances growth rate prediction and produces more realistic long-term successional trajectories.

Searching arXiv for the specific FINN meaning in forest modeling and nearby acronym usages. Forest Informed Neural Networks (FINN) are a hybrid dynamic forest modeling framework in which deep neural networks (DNNs) are embedded inside a mechanistic forest gap model and calibrated jointly with the remaining mechanistic parameters in a single end-to-end optimization. In the formulation introduced for dynamic vegetation modeling, the neural component does not operate as a post hoc correction layer; rather, it can replace selected demographic process equations—such as growth, mortality, or regeneration—while the surrounding forest dynamics model retains mechanistic state transitions, competition, and stand structure. The stated motivation is structural misspecification in Dynamic Vegetation Models (DVMs): even if parameters are well calibrated, fixed process forms may still be wrong, allowing a model to fit observations while “predicting the right things for the wrong reasons” (Pichler et al., 2 Aug 2025).

1. Definition, scope, and acronym ambiguity

Within the forest-dynamics literature considered here, FINN denotes Forest Informed Neural Networks and refers specifically to a hybrid modeling approach for dynamic forest models (Pichler et al., 2 Aug 2025). The framework was introduced to address a central limitation of DVMs and forest gap models: the mechanistic scaffold is often scientifically valuable, but the chosen analytical forms for processes such as growth, mortality, and recruitment may be too rigid.

The term is acronymically ambiguous across arXiv. In other papers, FINN refers to Fuzzy-Informed Neural Networks (Mazandarani et al., 2 May 2025), Fixed Integral Neural Networks (Kortvelesy, 2023), and Finite Volume Neural Network (Praditia et al., 2021). That ambiguity matters bibliographically, but not conceptually within the forest-modeling paper: there, FINN is unambiguously a hybrid forest dynamics framework rather than a fuzzy, integral, or PDE-discretization method.

The paper defines hybrid modeling in a strong sense. A DNN is allowed to replace one or more demographic process equations, but it remains embedded in a mechanistic simulator rather than being trained as an external plug-in estimator. This is presented as a response to three linked problems: conventional forest models are too rigid when a process is misspecified; externally fitted empirical submodels ignore interactions inside the full dynamic system; and inverse calibration over a small set of candidate functional forms is too restrictive for discovering the actual shape of a process function (Pichler et al., 2 Aug 2025).

2. Mechanistic forest-gap scaffold

FINN is built on a forest gap model inspired by JABOWA-type models. Trees are represented as cohorts within independent patches, with each cohort defined as

$$C_{i,p,c} = \bigl( \text{dbh}_{i,p,c}, \text{trees}_{i,p,c}, \text{species}_{i,p,c}, \text{cohortID}_{i,p,c} \bigr), \qquad c \in \{1,\dots,C_t\}.$$

The full state update is written as

$$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$

and the conceptual transition in the main text is

$$C_{t+1} = f(\text{regeneration}(env_t, regPar_s, light_t), \ \text{growth}(env_t, C_t, growthPar_s, light_t), \ \text{mortality}(env_t, C_t, mortPar_s, light_t)),$$

with competition/light given by

$light_t = \text{competition}(C_t, compPar_s).$

The timestep sequence is ecologically ordered. Growth is evaluated first, then mortality, then regeneration. In the appendix this is written through successive updates of light availability, growth rate, dbh, mortality, and recruits, including

$$\text{dbh}_{t+1} = \text{dbh}_t + \text{dbh}_t \, g_t.$$

This sequencing is not incidental: mortality can depend on growth, and regeneration occurs after mortality.

Competition is represented through available light. The paper describes light as being derived from basal area, weighted basal area, species-specific competitive strength compStr, tree-height differences, and a sigmoid shading function. The resulting available-light formulation is meant to capture canopy stratification: a focal cohort receives less light when more weighted basal area lies above it in the canopy (Pichler et al., 2 Aug 2025).

Environmental effects are modeled separately for regeneration, growth, and mortality through a linear predictor followed by a sigmoid,

$$\text{env}_{i,s}= \sigma\!\left( \beta_{s,0} +\beta_{s,1}\,x_{1,i} +\beta_{s,2}\,x_{2,i} +\cdots +\beta_{s,n}\,x_{n,i} \right),$$

yielding species-specific modifiers in $[0,1]$. In the fully mechanistic model, growth is the product of light, size, and environment,

$$g_{i,p,c} =\text{light}_{i,p,c}^{(\text{growth})}\, \cdot\text{size}_{i,p,c}^{(\text{growth})}\, \cdot\text{env}_{i,s}^{(\text{growth})},$$

while regeneration and mortality retain explicit stochastic forms,

$$r_{i,p,s}\sim\text{NBinom}\!\bigl(\lambda_{i,p,s},\,\phi\bigr), \qquad m_{i,p,c}\sim\text{Binom}\!\bigl(\pi_{i,p,c}\bigr).$$

The critique developed by the paper is that these mechanistic forms may be biologically plausible yet structurally wrong, especially the imposed separability and saturating light response in the growth equation (Pichler et al., 2 Aug 2025).

3. Hybridization of demographic processes

The key architectural move in FINN is to replace selected process equations with DNNs inside the state-transition system. The paper distinguishes three model classes:

Variant	Process specification	Role
Process-FINN	All demographic processes mechanistic	Fully mechanistic baseline
Hybrid-FINN	At least one process replaced by a DNN	Jointly calibrated hybrid model
Naïve DNN	Pure data-driven neural network on time-step responses	Non-mechanistic comparison

In the main Barro Colorado Island case study, only the growth process is replaced. The mechanistic growth equation

$$g_{i,p,c} =\text{light}_{i,p,c}^{(\text{growth})}\, \cdot\text{size}_{i,p,c}^{(\text{growth})}\, \cdot\text{env}_{i,s}^{(\text{growth})}$$

becomes

$$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$0

The paper also notes that mortality could be hybridized similarly, although that is not the main empirical configuration.

For a hybridized process, the DNN has 2 hidden layers, 50 nodes each, ReLU activations, and a dropout rate 20%. Species identity is integer-coded and passed through an embedding layer of dimension 2. For the growth DNN, the output activation is

$$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$1

which the paper reports had good convergence properties. Inputs are preprocessed by dividing dbh by 100, log-transforming tree variables, and embedding the species code (Pichler et al., 2 Aug 2025).

The defining methodological claim is joint calibration. The DNN is not pre-trained on process-level labels and then inserted into the simulator. Instead, its parameters are optimized through full-model demographic and stand-level outputs. This gives Hybrid-FINN a different epistemic role from plug-in estimators: the learned process must remain compatible with competition, mortality, regeneration, and multistep forest dynamics rather than only with isolated process observations.

4. Data, objective, and calibration procedure

The principal real-data application is the Barro Colorado Island (BCI) 50-ha plot in Panama, located at $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$2. The dataset contains seven inventories from 1985 to 2015, providing one initial state plus six subsequent time periods for calibration. After filtering, 281 tree and shrub species remained; these were aggregated either into 145 genera or into five plant functional types (PFTs), with the detailed analysis focusing on the PFT-based version (Pichler et al., 2 Aug 2025).

The 50-ha plot was divided into 500 patches, each $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$3 m $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$4. The manuscript mainly focuses on the variant with 5-year intervals and 25 patches per site. The response vector for each time, site, patch, and species comprises basal area, number of trees, average dbh, average relative growth rate, mortality rate, and regeneration rate. Environmental predictors include annual precipitation sum, annual solar radiation sum, annual mean relative humidity, annual maximum of daily temperature, annual minimum of daily temperature, and soil water potential from the late dry season map (Pichler et al., 2 Aug 2025).

The joint objective is described verbally rather than as one closed-form equation. What is specified is the loss composition: mean squared error (MSE) for dbh, basal area, mortality rate, and growth rate, together with negative binomial likelihoods for number of trees and recruits. Response weights are unequal: average dbh is weighted by 0.1, average growth by 10.0, and the remaining responses by 1.0. NA responses are masked in the joint loss.

Calibration is fully differentiable. The paper emphasizes that inputs, states, outputs, and parameters are represented as arrays; step functions are avoided; and differentiable approximations such as sigmoids are used for threshold-like effects. The implementation uses Torch for R with automatic differentiation. Optimization uses ADAM, learning rate 0.01, 8,000 epochs, and batch size 50%. A practical note from the supplementary material is that gradients are clipped after each observed response in time, because accumulating gradients over the entire series led to apparent vanishing-gradient problems and higher computational cost (Pichler et al., 2 Aug 2025).

Validation uses five-fold spatially blocked cross-validation, with folds constructed from the autocorrelation range of the soil water potential variogram via cv_spatial() from the blockCV package. For uncertainty estimation in Hybrid-FINN growth-response interpretation, the paper uses Monte Carlo Dropout with dropout set to $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$5, dropout left active at prediction time, and 100 ALE predictions used to compute means and standard deviations.

5. Empirical results and ecological interpretation

The paper first establishes a proof of concept in simulation. Data are generated from a Process-FINN model in which growth has a quadratic environmental niche curve, and three models are compared: M1, the true process model with quadratic growth-environment effect; M2, a misspecified process model with a linear growth-environment effect; and M3, Hybrid-FINN with DNN growth. The reported result is that Hybrid-FINN recovered the true functional form, whereas the misspecified mechanistic model did not. Hybrid-FINN also achieved better predictive performance for number of trees, growth rate, and mortality rate (Pichler et al., 2 Aug 2025).

On the BCI blocked spatial cross-validation, Hybrid-FINN gave the best overall predictive performance. The text reports that for Hybrid-FINN, basal area, dbh, number of trees, and regeneration achieved $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$6, while growth rate ranged roughly from $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$7 to $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$8, depending on PFT. Process-FINN also performed strongly on stand variables, often above $$C_{t+1} = \text{FINN}\bigl(C_t,\,\text{env}_t,\,\theta_j\bigr),$$9, but was less precise for growth and mortality, roughly $$C_{t+1} = f(\text{regeneration}(env_t, regPar_s, light_t), \ \text{growth}(env_t, C_t, growthPar_s, light_t), \ \text{mortality}(env_t, C_t, mortPar_s, light_t)),$$0. The Naïve DNN was somewhat competitive for growth rate but worse on stand variables, at roughly $$C_{t+1} = f(\text{regeneration}(env_t, regPar_s, light_t), \ \text{growth}(env_t, C_t, growthPar_s, light_t), \ \text{mortality}(env_t, C_t, mortPar_s, light_t)),$$1 for basal area and tree number and $$C_{t+1} = f(\text{regeneration}(env_t, regPar_s, light_t), \ \text{growth}(env_t, C_t, growthPar_s, light_t), \ \text{mortality}(env_t, C_t, mortPar_s, light_t)),$$2 for growth and mortality. The central empirical conclusion is that replacing growth with a DNN improved direct growth-rate prediction, stand-level prediction, regeneration prediction, and long-term successional behavior (Pichler et al., 2 Aug 2025).

Long-run behavior is a major part of the argument. The authors simulated 600 years of succession from the calibrated models. Hybrid-FINN produced more plausible successional trajectories across the five PFTs and an equilibrium resembling observed BCI dynamics under the disturbance regime of Rüger et al., whereas Process-FINN produced an implausible equilibrium, especially for the Short-lived breeder (SLB) PFT. This is presented as evidence that short-horizon fit can conceal structural misspecification.

The paper also reports that when growth was learned flexibly, other process parameters changed too, particularly mortality and recruitment parameters. This is interpreted as evidence for reduced compensatory bias: in the fully mechanistic model, a rigid growth equation had apparently forced other processes to absorb structural error.

Interpretability is pursued through accumulated local effect (ALE) plots. These indicate that the original mechanistic light response for growth—saturating and threshold-like—was likely misspecified. In contrast, the DNN in Hybrid-FINN learned a growth-light relationship that was described as mostly linear and non-saturating for all PFTs, while retaining the broad size effect. The paper further notes that fast growers and short-lived breeders showed some predicted growth even under very low available light. For short-lived breeders this may be ecologically plausible; for fast growers the paper treats the result more cautiously, suggesting that deep-shade predictions may be weakly supported by the data (Pichler et al., 2 Aug 2025).

6. Position within hybrid ecological modeling, limitations, and implications

FINN is positioned against two alternatives: the fully mechanistic forest model and the purely data-driven DNN. Relative to the former, its advantage is flexible process discovery under joint calibration. Relative to the latter, its advantage is that the DNN remains constrained by mechanistic state transitions, competition, and demographic coupling, which the paper associates with better stand-level consistency and more plausible succession trajectories (Pichler et al., 2 Aug 2025).

A central conceptual distinction is the rejection of plug-in estimation. The paper argues that process models trained separately from the full simulator are often inadequate because DVM outputs are emergent, process-level observations are interdependent, isolated calibration ignores compensatory interactions, and structural biases in one process affect the inferred role of others. FINN addresses this by calibrating neural and mechanistic components together in one optimization. This suggests that the framework is intended not merely as a predictive device, but as an inferential tool for diagnosing which process formulations are structurally wrong.

The limitations are explicit. The framework depends on replacing the right process; otherwise, structural error may simply move elsewhere. The data envelope constrains what a DNN can learn. Interpretability remains partial because the extracted process knowledge is visualized through ALE plots rather than converted into a closed-form symbolic equation. Environmental variation in BCI is limited, which the paper suggests may explain why between-PFT differences were captured better than within-PFT variation. The exact full joint objective is not written as a single equation. Most importantly, the paper does not directly demonstrate superiority under novel climate extrapolation. Rather, it argues that rigid process misspecification is especially harmful under extrapolation and that the more plausible succession trajectories of Hybrid-FINN are consistent with better generalization. That extrapolation advantage is therefore a reasoned hypothesis rather than a directly validated result (Pichler et al., 2 Aug 2025).

In synthesis, Forest Informed Neural Networks designate a differentiable hybrid forest dynamics framework in which a mechanistic forest gap model supplies the ecological scaffold while one or more selected demographic processes can be replaced by DNNs and trained jointly with the remaining mechanistic parameters. In the principal case study, replacing the growth process improved predictive performance on the BCI 50-ha plot, altered the inferred roles of mortality and recruitment, and exposed a likely misspecification in the mechanistic growth-light response. FINN is therefore best understood as a method for learning process structure from dynamic forest data without abandoning mechanistic realism, with the stated aim of improving both forecasting and ecological explanation in forest models under environmental change (Pichler et al., 2 Aug 2025).